Mathematics and Statistics

Upon completion of this course, the student will be able to:

• SLO 1: CORRECTLY USE THE ORDER OF OPERATIONS TO EVALUATE EXPRESSIONS. ACCURATELY COMPUTE PROBLEMS INVOLVING THE BASIC OPERATIONS OF ARITHMETIC (ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION, EXPONENTS, ORDER OF OPERATIONS) ON WHOLE NUMBERS, FRACTIONS, AND DECIMALS.
• Identify the prime numbers from 2 to 50. Use divisibility tests, factorization, and the concept of prime and composite to construct the least common multiple. Understand the process of rewriting a given number as the product of all distinct prime numbers.
• Express numeric information in one of the following three forms: fraction, percent, decimal.
• Convert numeric information into and out of scientific notation.
• Incorporate concepts of prime factorization and greatest common factor to simplify fractions.
• Evaluate problems involving ratios, proportions, and percents.
• Perform unit conversions for American measurements which involve length, capacity, weight, and times. Use the method of unit conversions to solve application problems.
• Demonstrate concepts of rounding and estimation of whole numbers and decimals to nearest place value.
• SLO 2: DEMONSTRATE THE ABILITY TO TRANSLATE MATHEMATICAL PROBLEMS IN WORD FORM TO AN EXPRESSION OR SINGLE VARIABLE EQUATION, AND SOLVE SINGLE VARIABLE ONE-STEP EQUATIONS.
• Translate simple English phrases and sentences into simple algebraic expressions and equations.
• Construct equations by translating information from word form to symbolic form with use of a variable.
• Set up applied problems involving ratios, proportions, and percents.
• Calculate solutions of one-step single variable equations.
• Solve applications problems involving whole numbers, fractions, decimals, ratios, proportions, and percents.
• Find perimeter and area of basic Euclidean and compound shapes.
• SLO 3: ANALYZE PATTERNS AND ORGANIZE MATHEMATICAL THOUGHTS TO INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL LIFE PROBLEM SOLVING.
• Apply mathematical concepts and patterns to new problems and new situations.
• Demonstrate ability to communicate mathematically by writing and presenting the work of the problems in an organized way.

Upon completion of this course, the student will be able to:

• SLO 1: ARTICULATE THE IMPORTANCE OF THE ORDER OF OPERATIONS AND HOW THEY RELATE TO THE REAL NUMBER SYSTEM, EXPRESSIONS, EQUATIONS AND EVALUATION OF MATHEMATICAL FORMULAS.
• Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
• Multiply and divide numbers expressed in scientific notation.
• Simplify expressions involving variables by adding, subtracting, multiplying, dividing, or reducing.
• Use and evaluate formulas with more than one variable.
• Demonstrate accurate use of the properties of real numbers and the exponent rules in addition, subtraction, and multiplication of polynomials.
• SLO 2: DEMONSTRATE THE ABILITY TO RECOGNIZE KEY WORDS OR PHRASES THAT WOULD GUIDE ONE THROUGH THE TRANSLATION OF A MATHEMATICAL PROBLEM IN WORD FORM TO AN ALGEBRAIC EXPRESSION OR EQUATION.
• Solve applied problems using signed numbers, variable expressions, scientific notation, and equations.
• Solve linear equations in one variable involving signed numbers, fractions, and decimals.
• Directly translate equations in word form to symbolic form with use of variables and solve them.
• SLO 3: INVESTIGATE AND MODEL REAL LIFE PHENOMENA THROUGH THE USE OF LINEAR EQUATIONS IN TWO VARIABLES AND THEIR CORRESPONDING GRAPHS (ALGEBRAICALLY AND GEOMETRICALLY), AND THINK CRITICALLY ABOUT HOW THE MATHEMATICS IS RELEVANT TO ONE’S LIFE.
• Find solutions to linear equations in two variables and plot these points on the two-dimensional coordinate system.
• Interpret graphs of two-dimensional data, such as bar graphs, line graphs and pie charts.
• SLO 4: UTILIZE AND APPLY THE METHOD OF DIMENSIONAL ANALYSIS (OR UNIT ANALYSIS) TO COMPARE AND CONVERT QUANTITIES.
• Solve applied problems using measurement conversions, proportions, and percent.
• Perform accurate computations involving measurement conversion.
• SLO 5: POSSESS THE ABILITY TO RECOGNIZE PATTERNS, ORGANIZE MATHEMATICAL THOUGHTS, AND INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL LIFE PROBLEM SOLVING.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the arithmetic level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the prealgebra level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the elementary algebra level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the intermediate algebra level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the statistics and/or geometry level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the non-transferable math level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the trigonometry, college algebra, and/or precalculus level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the differential and/or integral calculus level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the vector calculus, differential equations, and/or linear algebra level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO(1): BUILD STUDY SKILLS AND LEARNING STRATEGIES NEEDED FOR CONTINUED SUCCESS IN MATHEMATICS EDUCATION.
• demonstrate improved math study skills.
• exhibit increased confidence level in approaching mathematics.
• SLO(2): UTILIZE MATHEMATICAL SKILLS IN A VARIETY OF CONTEXTS.
• demonstrate an improved performance at the transferable math level.
• SLO(3): FORMULATE STRATEGIES AND CHOOSE AN APPROPRIATE COMBINATION OF TECHNIQUES FOR SOLVING APPLIED PROBLEMS.
• employ problem solving strategies to improve specific course skills.

Upon completion of this course, the student will be able to:

• SLO 1: UTILIZE MATHEMATICAL TERMINOLOGY AND ARTICULATE MATHEMATICAL CONCEPTS APPROPRIATE TO THE RELEVANT AREA OF STUDY.
• Understand the terms and concepts included in relevant area of review/study.
• SLO 2: EMPLOY MATHEMATICAL SKILLS AT A MASTERY LEVEL.
• Practice using the skills being reviewed.
• Demonstrate competency at an appropriate mastery level.
• SLO 3: ANALYZE A MATHEMATICAL PROBLEM AND APPLY AN APPROPRIATE SET OF PROBLEM-SOLVING SKILLS.
• Complete critical thinking exercises that apply relevant skills to the area of review/study.

Upon completion of this course, the student will be able to:

• SLO#1: DEMONSTRATE AN UNDERSTANDING OF THE LEARNING PROCESS AS IT APPLIES TO MATHEMATICS AS SHOWN BY:
• Analyzing his/her current study habits and attitudes as they pertain to math courses
• Distinguishing the differences between learning mathematics and learning other subjects
• Classifying individual learning styles
• SLO#2: RECOGNIZE AND APPLY VARIOUS STRATEGIES APPLICABLE TO A MATHEMATICS COURSE, SUCH AS:
• Listening and note-taking skills as they pertain to math courses
• Applying study techniques, including but not limited to, how to read a math textbook and using math homework as a learning tool
• Applying test-taking strategies and techniques as they pertain to math courses
• Applying memorization techniques as they pertain to math courses
• SLO#3: DEVELOP STRATEGIES TO LOWER ONE'S MATH ANXIETY LEVEL BY:
• Examining and assessing the sources and symptoms of math anxiety
• Developing methods for reducing math anxiety to a productive level

Upon completion of this course, the student will be able to:

• SLO#1: Use increased computational skills and number sense, recognize the order of operations and properties of real numbers; include evaluating various mathematical formulas and extending operations to variable expressions and combining like terms.
• Simplify expressions using the order of operations and basic properties of real numbers.
• Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
• Multiply and divide numbers expressed in scientific notation.
• Use and evaluate formulas with more than one variable.
• SLO#2: Solve first degree equations, inequalities and applications.
• Identify the types of equations including conditional equations, contradiction and identity and techniques for their solution.
• Solve linear inequalities and write the solution in both set-builder and interval notation.
• Apply problem solving skills to construct equations and inequalities for application problems and solve the applications by solving the equations or inequalities and appropriately interpreting the results.
• SLO#3: Identify and analyze linear equations, and graphs of linear equations and linear inequalities.
• Interpret the slope of a line as a rate of change and graph a line.
• Generate an algebraic model for data that follows linear behavior and interpret the result of this model. Applications of linear models include linear growth, linear depreciations and rates.
• SLO#4: Apply mathematical terminology, symbols and operations to develop and extend arithmetic operations on polynomials and to evaluate polynomial expressions.
• Evaluate and expand polynomial expressions and expressions written in scientific notation.
• Apply rules of exponents (including negative exponents) to simplify algebraic expressions.
• Demonstrate proficiency in all arithmetic operations on polynomials, particularly multiplying using FOIL.
• Use operations on polynomials to solve certain polynomial equations and applications.
• SLO#5: Understand the concept of prime polynomials and factoring polynomials into primes using various techniques.
• Factor out common factors and factor by grouping.
• Factor the difference of two squares and factor trinomials including perfect square trinomials.
• Solve polynomial equations by factoring and using the zero factor property.
• Think critically and abstractly by modeling an application problem using a polynomial equation to solve and interpret the result.
• SLO#6: Simplify, combine and evaluate rational expressions using the operations of arithmetic.
• Multiply and divide rational expressions and incorporate factoring to simplify to lowest terms.
• Add and subtract rational expressions using the algebraic method and least common denominator.
• Solve rational equations by multiplying by the least common denominator.
• Use an appropriate rational equation to model an application problem to solve and interpret the results.
• SLO #7: Solve systems of linear equations and systems of linear inequalities as well as their applications and effectively organize, present, and summarize the quantitative information using algebraic, numerical and graphical methods.
• Calculate the solution to a 2x2 system of linear equations using the methods of graphing, substitution, and elimination, and identify the types of 2x2 systems.
• Construct a system of linear equations for applications and solve the applications by solving the system and appropriately interpret the solution.
• Compute the solution to a system of linear inequalities using a graph and describe the meaning of this solution.
• SLO#8: Demonstrate with proficiency how to use arithmetic operations on radicals and simplify radical expressions.
• Simplify different types of radicals, rationalize denominators and combine radicals when it is appropriate.
• Solve radical equations and evaluate radical expressions.
• Solve applied problems using radical equations and using the Pythagorean Theorem to solve triangles and applications.
• Verify how to extend the definition of an exponent to a rational exponent and interpret a rational exponent as a radical.
• Use radicals to solve quadratic equations by taking roots, completing the square and using the quadratic formula and employ quadratic equations in various applications.

Upon completion of this course, the student will be able to:

• SLO #1: DEMONSTRATE UNDERSTANDING OF THE STEP-BY-STEP DEVELOPMENT OF A LOGICAL MATHEMATICAL SYSTEM
• Clearly state and correctly use definitions, postulates, and theorems.
• Write 2-column direct proofs, indirect proofs, and analytic proofs using the definitions, postulates, and theorems of Euclidean geometry
• SLO #2: DEVELOP PROBLEM-SOLVING SKILLS USED TO SOLVE CALCULATIONS.
• Find missing side lengths and angle measures in a diagram using appropriate theorems.
• Find areas of planar figures, surface area and volume of solids.
• Analyze diagrams in the Cartesian coordinate system.
• Develop a fundamental understanding and application of right triangle trigonometry.
• SLO #3: CONSTRUCT PROOFS TO VERIFY GEOMETRIC RELATIONSHIPS.
• Write 2-column direct proofs, indirect proofs, and analytic proofs using the definitions, postulates, and theorems of Euclidean geometry
• SLO #4: PERFORM GEOMETRIC CONSTRUCTIONS USING A COMPASS AND STRAIGHTEDGE, AND USE A PROTRACTOR TO MEASURE ANGLES
• Construction of parallel lines, perpendicular lines
• Bisect an angle and a line segment
• Copying an angle
• Use a protractor to measure angles

Upon completion of this course, the student will be able to:

• <b>SLO 1:</b> Identify and analyze linear behavior, models, and graphs of linear equations and linear inequalities. Utilize the properties of linear equations to solve linear inequalities, and solve absolute value equations and inequalities <ul><li>interpret the slope of a linear equation as a rate of change.</li><li>generate an algebraic model for data that follows linear behavior and interpret the results of this model.</li><li>sketch the graph of a linear inequality using its algebraic representation.</li></ul>
• <b>SLO 2:</b> Solve systems of linear equations and systems of linear inequalities as well as their applications graphically and algebraically <ul><li>calculate the solution to 2x2 and 3x3 systems of linear equations by using substitution, elimination, and graphs (for 2x2 systems), as well as determine whether a system is inconsistent, consistent and independent, or dependent.</li><li>construct systems of linear equations for applications and find their solution.</li><li>compute the solution to a system of linear inequalities using a graph and describe the meaning of this solution.</li></ul>
• <b>SLO 3:</b> Recognize the behavior of exponential and logarithmic functions and their graphs. Apply the properties of exponential and logarithmic expressions to simplify and solve equations involving such expressions <ul><li>evaluate algebraic expressions involving exponents and logarithms and convert between these two types of expressions.</li><li>produce the algebraic model of an exponential function using data points and use properties of exponential functions to derive conclusions.</li><li>employ the properties of exponents and logarithms to solve equations involving exponential and logarithmic expressions.</li><li>draw the graph of exponential and logarithmic functions using both point plotting and the properties of transformations.</li><li>consolidate and expand logarithmic expressions using the properties of logarithms.</li></ul>
• <b>SLO 4:</b> Identify, simplify, evaluate, and graph quadratic functions using the properties of quadratic functions and transformations <ul><li>demonstrate the properties of transformations by graphing a quadratic function, identifying the vertex and the intercepts with the axes.</li><li>choose from among factoring (and using the Zero Factor Property), extraction of roots, completing the square, or the quadratic formula to solve a quadratic equation.</li><li>apply properties of quadratic functions to create and solve quadratic models and to derive conclusions about the solutions.</li></ul>
• <b>SLO 5:</b> Simplify polynomial expressions, evaluate polynomial functions, and solve equations involving polynomial expressions and their applications <ul><li>investigate polynomial division by performing long division on polynomial expressions.</li><li>extend factoring techniques to include the sum and difference of cubes.</li><li>adapt factoring to include expressions that are quadratic in form.</li><li>graph a circle given its equation in standard form as well as use the distance and midpoint formulas to find the equation of a circle given conditions.</li></ul>
• <b>SLO 6:</b> Simplify and solve rational and radical expressions and equations (including those with higher roots) <ul><li>perform arithmetic on rational and radical expressions and write results in simplified form.</li><li>simplify complex fractions.</li><li>manipulate equations involving rational or radical expressions to arrive at a non-extraneous solution.</li><li>recognize and solve applications that involve rational or radical expressions.</li></ul>
• <b>SLO 7:</b> Use, interpret, and simplify functions, inverse functions, and combination functions <ul><li>understand and use the definition of a function and interpret the difference between a relation and a function</li><li>describe the domain and range of functions.</li><li>compose the graph of a function from tabular data, a word problem, or algebraic form.</li><li>perform composition of functions as well as arithmetic on combinations of functions.</li><li>find the inverse of a function algebraically and graphically</li><li>interpret the meaning of the inverse in application problems</li></ul>

Upon completion of this course, the student will be able to:

• SLO 1: ANALYZE AND FIND BEST FIT EQUATIONS FOR REAL WORLD DATA GIVEN IN MANY FORMS.
• Organize information into any/all of its four forms: words, data tables, graphs, and algebraic equations.
• Design an accurately scaled and labeled scatterplot of data, use a best fit line to examine linear trends, interpret the meaning of slope as a rate of change.
• Accurately graph and analyze functions; use linear, quadratic, and exponential functions to model real world applications and interpret real data.
• Distinguish arithmetic and geometric progressions; develop formulas for arithmetic and geometric sequences; use summation notation to calculate finite series.
• SLO 2: SOLVE EQUATIONS AND INEQUALITIES WHICH COME FROM APPLIED PROBLEMS.
• Simplify and evaluate rational and radical expressions, compositions, exponentials and logarithms; solve linear, quadratic, rational, radical, exponential, logarithmic, and literal equations.
• Accurately solve absolute value inequalities and systems of linear equations; use systems of equations to solve applied problems.

Upon completion of this course, the student will be able to:

• SLO 1: EXPLORE THE ORIGINS AND CULTURAL CONTRIBUTIONS OF EARLY NUMBER SYSTEMS INCLUDING WRITING AND CALCULATING IN OTHER SYSTEMS
• Translate numbers in early and modern numeration systems.
• Examine the diverse cultural history of early and modern numeration systems.
• SLO 2: ENCODE AND DECODE USING CRYPTOGRAPHY & OTHER CODING SYSTEMS
• Calculate and translate numerical information in non-decimal base systems fundamental to computer programming and other digital systems.
• Apply encryption algorithms for encoding and decoding used to protect the security of information interchange.
• Perform arithmetic operations in modular systems used in modern business applications such as bar codes, UPC codes, ISBN numbers.
• SLO 3: CONSTRUCT AND TEST THE VALIDITY OF LOGIC STATEMENTS USING CONNECTIVES, TRUTH TABLES AND VENN DIAGRAMS
• Construct truth tables, identify the hierarchy of connectives, and use truth tables to classify statements.
• Test the validity of arguments by using common argument forms.
• SLO 4: EXPLORE THE TERMINOLOGY, METHODOLOGY, GRAPHICAL DISPLAYS AND CONCLUSIONS OF MODERN STATISTICS
• Compare methods of modern data collection and other sampling methods.
• Organize, display, describe and compare one-variable data.
• Organize, display, describe and compare two variable data.
• Apply statistical methods for computing confidence interval estimates and interpreting margin of error.
• SLO 5: DEMONSTRATE THE USE OF MATHEMATICS AND CRITICAL THINKING IN CONTEMPORARY VOCATIONAL AND TECHNICAL FIELDS

Upon completion of this course, the student will be able to:

• SLO #1: Actively engage in intellectual inquiry beyond that required in order to pass a course of study (College Wide Learning Outcome – Area 4).
• Discuss and outline a proposal of study (that can be accomplished within one semester term) with a supervising instructor qualified within the discipline.
• Design an independent study (to be completed individually or by collaboration of a small group) to foster special knowledge, skills, and experience that are not available in any one regularly scheduled course.
• Use information resources to gather discipline-specific information.
• SLO #2: Utilize modes of analysis and critical thinking to apply theoretical perspectives and/or concepts in the major discipline of study to significant problems and/or educational activities (College Wide Learning Outcome – Area 3).
• Analyze and apply the knowledge, skills and experience that are involved in the independent study to theoretical perspectives and/or concepts in the major discipline of study.
• Explain the importance of the major discipline of study in the broader picture of society.
• SLO #3: Communicate a complex understanding of content matter of the major discipline of study (College Wide Outcome – Area 3).
• Demonstrate competence in the skills essential to mastery of the major discipline of study that are necessary to accomplish the independent study.
• SLO #4: Identify personal goals and pursue these goals effectively (College Wide Outcome – Area 4).
• Utilize skills from the “academic tool kit” including time management, study skills, etc., to accomplish the independent study within one semester term.

Upon completion of this course, the student will be able to:

• SLO 1: Categorize and analyze mathematical objects and apply them to real life problems
• Define and setup tables, diagrams, graphs, and matrices
• SLO 2: Solve mathematical problems from different branches of mathematics
• Manipulate and solve problems relating to algebra
• Apply basic geometric axioms, definitions, and theorems to solve geometric problems
• Recognize principles of counting techniques to determine number of ways to select members from a group for a specific task
• Compute mean, median, mode, range, standard deviation, and variance of a set of data
• SLO 3: Interpretations of mathematical objects in a variety of analytical settings and performing different operations to combine these objects
• Recognize different representations of sets and performing different set operations to combine sets
• Apply the logic properties to assess the validity of an argument
• SLO 4: Apply the mathematical concepts or objects to assess a situation , make decisions, and solve the real life problems
• Assess the risks and rewards of credit cards and investments, and select the optimal path for a delivery route
• Create an efficient schedule, select a fair method for dividing valuable assets, and evaluate the efficiency of an algorithm
• SLO 5: Defend some aspects of the mathematics used in real life applications
• Investigate and solve real life problems such as home mortgage loans and student loans
• Pursue the meaning of mathematics through the history of different numeration system and the progression of mathematics

Upon completion of this course, the student will be able to:

• SLO(1) EXPLORE MATHEMATICAL PATTERNS AND MAKE CONJECTURES
• explore mathematical relationships inherent in problems and situations from new branches of mathematics (such as number theory or sequences and series) by recognizing patterns and connections to previously encountered topics.
• solve applied problems by recognizing connections between methods of solution employed in various mathematical fields.
• formulate clearly written conjectures based on exploration of mathematical situations.
• SLO(2) PROVE OR DISPROVE CONJECTURES
• prove or disprove conjectures about mathematical relationships and content.
• develop skills in logical reasoning and making logical explanations.
• SLO(3) DEVELOP STRATEGIES FOR INDEPENDENT PROBLEM SOLVING
• explore mathematical problems independently, extending their solutions to questions not necessarily posed by the instructor.
• develop and explain a mathematical solution to a problem not previously encountered by the student.

Upon completion of this course, the student will be able to:

• SLO 1: SUMMARIZE THE HISTORICAL DEVELOPMENT OF NUMERATION SYSTEMS, INCLUDING AN EXAMINATION OF THE BASE TEN NUMERATION SYSTEM AND AN ANALYSIS OF PLACE VALUE SYSTEMS IN GENERAL USING EXPONENT AND PLACE VALUE NOTATION.
• Perform calculations with place value systems.
• SLO 2: EVALUATE THE EQUIVALENCE OF NUMERIC ALGORITHMS AND EXPLAIN THE ADVANTAGES AND DISADVANTAGES OF EQUIVALENT ALGORITHMS IN DIFFERENT CIRCUMSTANCES.
• Apply algorithms from number theory to determine divisibility in a variety of settings.
• SLO 3: ANALYZE LEAST COMMON MULTIPLES AND GREATEST COMMON DIVISORS AND THEIR ROLE IN STANDARD ALGORITHMS.
• Explain the concept of rational numbers, using both ratio and decimal representations; analyze the arithmetic algorithms for these two representations; and justify their equivalence.
• SLO 4: ANALYZE THE STRUCTURE AND PROPERTIES OF WHOLE, RATIONAL, AND REAL NUMBER SYSTEMS; DEFINE THE CONCEPT OF RATIONAL AND IRRATIONAL NUMBERS, INCLUDING THEIR DECIMAL REPRESENTATION; AND ILLUSTRATE THE USE OF A NUMBER LINE REPRESENTATION.
• Develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation.
• SLO 5: APPLY BASIC TOOLS SUCH AS SETS, FUNCTIONS, AND LOGIC TOGETHER WITH DEDUCTIVE OR INDUCTIVE REASONING TO SOLVE PROBLEMS FROM AN ELEMENTARY TO ADVANCED LEVEL OF MATH.
• Develop activities implementing curriculum standards.

Upon completion of this course, the student will be able to:

• SLO 1: Analyze and investigate properties of functions<ul><li>Perform arithmetic and algebraic operations on functions.</li><li>Compute the domain and range of functions.</li><li>Graph transformations of functions.</li><li>Investigate function inverses.</ul>
• SLO 2: Synthesize results from the graphs and equations of functions;<ul><li>Given the graph of a function, indicate function values and when functions attain specific values.</li><li>In applications, use functions to predict outcomes and qualitatively analyze information.</li></ul>
• SLO 3: Solve, and use in applications, equations.<ul><li>Solve rational, radical, linear, absolute value, polynomial, exponential, and logarithmic equations.</li><li>Use these equations to attain realistic solutions to real-world problems.</li></ul>
• SLO 4: Solve linear and nonlinear systems of equations and inequalities;<ul><li>Solve 2x2 and 3x3 systems of linear equations.</li><li>Graph solution sets to linear inequalities.</li></ul>
• SLO 5: Apply functions and other algebraic techniques to model real-world applications;
• SLO 6: Demonstrate the relationship between functions and their inverses graphically and algebraically;
• SLO 7: Apply rigid and non-rigid transformations to the graphs of functions.<ul><li>Perform all rigid transformations on graphs of functions.</li><li>Apply non-rigid vertical transformations on functions.</li></ul>

Upon completion of this course, the student will be able to:

• SLO#1: Cite the six fundamental trigonometric functions and be able to interpret and evaluate them
• define the trigonometric functions using right triangles and/or the unit circle
• evaluate the trigonometric functions using reference angles and special triangles
• calculate the values of the trigonometric functions using a calculator with angles in both degrees and radians
• SLO#2: Solve application problems by modeling them with appropriate functions
• recognize what type of function might be best to use in a given situation to model an applied problem
• distinguish between the various ways of solving application problems with trigonometric methods including the use of right triangles, oblique triangles, the law of sines, and the law of cosines
• use a polynomial, rational, exponential, logarithmic, or trigonometric function to model and solve an application
• analyze applications involving exponential and logarithmic growth and decay
• SLO#3: Graph a library of functions including trigonometric, polynomial, rational, absolute value, exponential, and logarithmic functions
• recognize a base graph when given the formula for a complex function
• employ the use of translations, reflections and nonrigid transformations to graph a function once the base graph is known
• express the domain and range of a function in interval notation given a formula or a graph of the function
• recognize important characteristics of graphs of functions including asymptotic behavior, periodic behavior, zeros, and end behavior patterns
• identify a function as even, odd or neither and be able to prove result
• extend quadratic functions to include methods for finding vertices, finding and interpreting intercepts, and minimizing and maximizing functions
• graph points and curves in the polar coordinate system
• SLO#4: Categorize types of equations, systems and inequalities and methods used to solve them
• employ algebraic and graphical methods to solve polynomial, rational, and absolute value equations, systems and inequalities
• use matrix methods to solve systems of equations including the Gauss-Jordan method
• recognize when to use logarithms to solve an equation
• integrate algebraic techniques with known identities to prove trigonometric identities
• solve trigonometric equations and be able to express solutions when restricted to an interval or when there are an infinite number of solutions
• use inverse trigonometric functions to solve an equation
• use sign graphs and graphs of functions to solve inequalities
• SLO#5: Manipulate mathematical expressions to accomplish a specific goal
• simplify and factor expressions when solving equations, working with rational expressions, and finding the difference quotient
• employ properties of exponents and logarithms to manipulate expressions
• use trigonometric identities to rewrite or expand an expression and to do proofs
• write equations of conic sections in standard form to graph them
• analyze conic sections using foci, directrices and asymptotes
• convert points and equations from polar coordinates to rectangular coordinates and the reverse

Upon completion of this course, the student will be able to:

• SLO 1: SIMPLIFY ALGEBRAIC EXPRESSIONS AND SOLVE ALGEBRAIC EQUATIONS RELATED TO BUSINESS PROBLEMS.
• Formulate expressions and equations important in business (e.g., profit, average cost, supply and demand, etc.).
• Understand the concepts and definitions of intercepts and the intersection point between two lines.
• SLO 2: EVALUATE LIMITS AND DERIVATIVES OF ALGEBRAIC, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS.
• Use the definition of the limits to calculate the limits of algebraic, exponential, and logarithmic functions.
• Use graphs, tables, and a variety of algebraic skills to compute limits.
• Calculate derivatives of algebraic functions using the Power, Product, Quotient, and Chain rules.
• SLO 3: APPLY THE LIMITS AND DERIVATIVE TO BUSINESS APPLICATIONS.
• Interpret the derivative to solve the optimization problems.
• Apply the derivative to marginal cost, revenue, and profit analysis.
• SLO 4: DISTINGUISH BETWEEN DEFINITE AND INDEFINITE INTEGRALS AND UNDERSTAND THE RELATIONSHIP BETWEEN THE INTEGRAL AND ANTIDERIVATIVE.
• Evaluate definite integrals using the Fundamental Theorem of Calculus.
• Calculate antiderivatives of various functions using substitution, integration by parts, and other methods.
• Formulate solutions to applications in business, such as consumer and producer surplus models that require integration.
• SLO 5: STUDY MULTIVARIABLE FUNCTIONS.
• Analyze functions of several variables and their relevance to business.
• Use partial derivatives to find extreme values of functions.
• Apply Lagrange multipliers and Least Squares Method to predict business models.

Upon completion of this course, the student will be able to:

• SLO 1: Understand and apply the mathematics of finance
• Calculate and interpret simple, compound, and continuously compounded interest
• Calculate monthly payments and form an amortization schedule
• Recognize and use the correct formulas for present value, future value, annuities and sinking funds
• SLO 2: Calculate and interpret solutions to linear programming problems
• Graph and solve a system of linear inequalities for corner points and feasible region
• Solve applications of linear programming
• SLO 3: Analyze business and economic problems
• Graph and apply linear, quadratic, power, polynomial, rational, exponential, and logarithmic functions in business application models
• Analyze formulas, graphs, tables, and data sets in order to make predictions and to form conclusions
• SLO 4: Calculate and interpret rates of change in business
• Calculate limits and derivatives using the power rule, product rule, quotient rule, and chain rule
• Calculate derivatives of exponential and logarithmic functions
• Apply the derivative to optimize functions and applications to marginal analysis
• Apply the derivative to minimize and maximize business applications such as cost, revenue, and profit functions

Upon completion of this course, the student will be able to:

• SLO#1: EXAMINE THE GRAPHS AND LIMITS OF FUNCTIONS.
• Examine elementary functions and their graphs.
• Explore discrete models of exponential growth and decay, log-log/semi-log graphing, discrete biological models, fixed points/steady states, stability, periodic solutions and chaos.
• Evaluate and interpret limits: the definition of limits, continuity of functions, the intermediate value theorem, the bisection method, trigonometric limits, and limits at infinity.
• SLO #2: DIFFERENTIATE POLYNOMIAL, RADICAL, TRIGONOMETRIC, LOGARITHMIC, AND EXPONENTIAL FUNCTIONS.
• Explore the definition of derivative, geometric interpretation of derivative, the derivative as rate of change, the differentiability of functions, and the properties of derivatives.
• Learn and apply the basic rules for differentiation: the power rule, product rule, quotient rule and chain rule.
• Differentiate exponential, logarithmic and trigonometric functions.
• Extend differentiation methods to include implicit differentiation, related rates, higher-order derivatives, linear approximation and L’Hopital’s Rule.
• SLO#3: GRAPH, ANALYZE & OPTIMIZE FUNCTIONS.
• Calculate maxima and minima and explore monotonicity and concavity of elementary functions and other graphs including sigmoidal curves.
• Test the stability of fixed points in differential equations and apply the Newton-Raphson method for numerical root finding.
• SLO#4: APPLY DERIVATIVES TO APPLICATIONS IN BIOLOGY AND MEDICINE.
• Apply the concepts and principles of calculus to find rates of change in populations, bacteria, blood flow, ecology, learning, drug absorption and other biological and life science situations.
• SLO#5: INTEGRATE BASIC ELEMENTARY FUNCTIONS.
• Apply the Fundamental Theorem of Calculus to the evaluation of definite integrals.
• Integrate functions using the power rule, substitution, integration by parts, and partial fraction decomposition.
• Explore numerical integration, tables of integrals and Taylor approximation.
• SLO #6 SOLVE DIFFERENTIAL EQUATIONS.
• Solve initial value ordinary differential equations and differential equations related to biological models of growth and decay.
• Solve first-order differential equations using integrating factors.

Upon completion of this course, the student will be able to:

• SLO #1: SOLVE SYSTEMS OF EQUATIONS.
• Use matrices, matrix operations and determinants to solve systems of linear equations.
• Compute eigenvalues and eigenvectors for square matrices.
• Solve linear systems of ordinary differential equations (ODEs).
• Apply systems of linear differential equations to problems in biology and medicine.
• Solve nonlinear systems of ordinary differential equations and apply these methods to biological models.
• SLO #2: EXLORE FUNCTIONS OF TWO OR MORE VARIABLES.
• Evaluate and interpret limits and continuity of multivariate functions.
• SLO #3: DIFFERENTIATE MULTIVARIATE FUNCTIONS.
• Compute partial derivatives of functions of several variables.
• Interpret partial derivatives as slopes and rates of change.
• Apply the chain rules for multivariate functions and parameterized curves.
• Implicitly differentiate multivariate functions.
• SLO #4: ANALYZE & OPTIMIZE MULTIVARIATE FUNCTIONS.
• Graph functions of two variables and calculate equations of tangent planes to the graph.
• Find extrema of multivariate functions, identify local and global extrema and solve applications involving extrema.
• Optimize multivariate functions and optimize multivariate functions with constraints.
• Find the gradient vector and directional derivatives and interpret directional derivatives as slopes and rates of change.
• SLO #5: INTEGRATE MULTIVARIATE FUNCTIONS.
• Compute and evaluate double integrals on multivariate functions.
• Solve applications of double integrals.
• SLO #6: COMPUTE PROBABILITIES FOR BIOLOGICAL SITUATIONS AND OTHER CHANCE OUTCOMES.
• Apply counting principles, permutations, and combinations to biological situations.
• Compute probabilities using basic probability rules, conditional probability, independence, Bayes’ formula, and Bayesian probability and apply these methods to biological models and events.
• Explore probability distributions of discrete random variables and use discrete probability distributions to solve applications in biology and medicine.

Upon completion of this course, the student will be able to:

• SLO1: WORK WITH MATHEMATICAL EXPRESSIONS AND SOLVE MATHEMATICAL EQUATIONS.
• Evaluate, expand, and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
• Expand binomial expressions by using the binomial theorem.
• SLO2: GRAPH AND ANALYZE FUNDAMENTAL MATHEMATICAL FUNCTIONS AND EQUATIONS IN BOTH RECTANGULAR AND POLAR COORDINATE SYSTEMS.
• Graph and analyze polynomial, rational, absolute value, exponential, logarithmic, trigonometric functions, and inverse trigonometric functions, as well as conic sections, involving algebraic transformations (shifts, scale factors, reflections, and absolute value) in rectangular coordinate system.
• Graph and analyze polar equations.
• Use algebraic techniques in combination with a graphing calculator to correctly analyze the graphs of functions composed of several basic functions.
• Model and solve "real world" problems using functions.
• SLO3: WORK WITH VECTORS, MATRICES, SEQUENCES, AND SERIES.
• Demonstrate the use and properties of vectors, matrices, sequences, and series.
• Model and solve "real world" problems using vectors, matrices, sequences, and series.
• SLO4: USE CORRECT LOGIC IN REASONINGS
• Prove mathematical facts using algebraic manipulations, fundamental trigonometric identities, direct proof, indirect proof, and the principle of mathematical induction.
• Identify and recognize different types of problems to be solved; select appropriate mathematical models and devise logical plans to solve the problems.

Upon completion of this course, the student will be able to:

• SLO 1: Analyze and investigate properties of functions.
• Objective 1a: Synthesize connections between equations of functions and their graphs.
• Objective 1b: Apply transformations to the graphs of functions.
• Objective 1c: Recognize the relationship between a function and its inverse both graphically and algebraically.
• Objective 1d: Apply functions and other algebraic techniques to model real world STEM applications.
• SLO 2: Apply solution techniques to equations and interpret results.
• Objective 2a: Solve equations and applications involving rational, linear, polynomial, radical, absolute value, exponential, and logarithmic equations.
• Objective 2b: Solve systems of equations and inequalities.
• Objective 2c: Apply techniques for determining zeros of polynomials and roots of equations.
• SLO 3: Analyze conic sections.
• Objective 3a: Construct an algebraic representation of the equation of a conic from a graph.
• Objective 3b: Distinguish the differences between algebraic representations of conic sections.
• Objective 3c: Sketch the graph of the equation of a given conic section.
• SLO 4: Investigate sequences and series.
• Objective 4a: Investigate arithmetic and geometric sequences.
• Objective 4b: Use formulas to find the sum of both finite and infinite series.

Upon completion of this course, the student will be able to:

• SLO 1: Investigate angular measure and trigonometric functions.
• Objective 1a: Identify special triangles and their related angle and side measures.
• Objective 1b: Evaluate the trigonometric function of angles in degree and radian measure.
• Objective 1c: Manipulate and simplify trigonometric expressions.
• Objective 1d: Calculate powers and roots of complex numbers using DeMoivre’s Theorem.
• SLO 2: Graph trigonometric functions and use identities to solve trigonometric equations.
• Objective 2a: Solve trigonometric equations, triangles, and applications.
• Objective 2b: Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs.
• Objective 2c: Evaluate and graph inverse trigonometric functions.
• SLO 3: Use trigonometric identities.
• Objective 3a: Prove trigonometric identities.
• Objective 3b: Use trigonometric identities to graph trigonometric functions.
• Objective 3c: Implement the use of trigonometric identities to solve trigonometric equations.
• SLO 4: Graph polar functions and parametric curves.
• Objective 4a: Graph basic parametric curves with proper paths of travel by plotting points or eliminating parameters.
• Objective 4b: Convert between polar and rectangular coordinates and equations.
• Objective 4c: Graph polar equations.
• SLO 5: Use trigonometric functions in applications.
• Objective 5a: Investigate arc length, linear velocity, and angular velocity.
• Objective 5b: Represent a vector (a quantity with magnitude and direction) in the form and ai + bj.
• Objective 5c: Build and solve applications using sinusoidal models.

Upon completion of this course, the student will be able to:

• SLO 1: Analyze and investigate properties of functions.
• Synthesize connections between equations of functions and their graphs.
• Apply transformations to the graphs of functions and relations.
• Recognize the relationship between functions and their inverses graphically and algebraically.
• Apply functions to model real world applications.
• SLO 2: Apply solution techniques to equations and interpret results.
• Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, logarithmic, and trigonometric, and solve linear, nonlinear, and absolute value inequalities.
• Solve systems of equations and inequalities.
• Apply techniques for determining zeros of polynomials and roots of equations.
• SLO 3: Analyze conic sections.
• Construct an algebraic representation of the equation of a conic from a graph.
• Distinguish the differences between algebraic representations of conic sections.
• Accurately graph the equation of a given conic section.
• SLO 4: Investigate sequences and series.
• Investigate arithmetic and geometric sequences.
• Use formulas to find the sum of both finite and infinite series.
• SLO 5: Investigate angular measure and trigonometric functions.
• Identify special triangles and their related angle and side measures.
• Evaluate the trigonometric function of angles in degree and radian measure.
• Manipulate and simplify trigonometric expressions.
• Calculate powers and roots of complex numbers using DeMoivre’s Theorem.
• SLO 6: Graph trigonometric functions and use identities to solve trigonometric equations.
• Solve trigonometric equations, triangles, and applications.
• Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs.
• Evaluate and graph inverse trigonometric functions.
• SLO 7: Use trigonometric identities.
• Prove trigonometric identities.
• Use trigonometric identities to graph trigonometric functions.
• Implement the use of trigonometric identities to solve trigonometric equations.
• SLO 8: Graph polar functions and parametric curves.
• Graph basic parametric curves with proper paths of travel by plotting points or eliminating parameters.
• Convert between polar and rectangular coordinates and equations.
• Graph polar equations.
• SLO 9: Use trigonometric functions in applications.
• Investigate arc length, linear velocity, and angular velocity.
• Represent a vector (a quantity with magnitude and direction) in the form and ai + bj.
• Build and solve applications using sinusoidal models.

Upon completion of this course, the student will be able to:

• SLO 1: SIMPLIFY ALGEBRAIC AND TRIGONOMETRIC EXPRESSIONS ENCOUNTERED IN THE EARLY WEEKS OF CALCULUS I.<ul><li>Simplify expressions involving negative rational exponents, compound fractions, rationals, radicals, absolute values, and trigonometric functions.</li></ul>
• SLO 2: SOLVE EQUATIONS AND INEQUALITIES ENCOUNTERED THROUGHOUT CALCULUS I.<ul><li>Solve equations that are quadratic-in-form, as well as those involving negative rational exponents.</li><li>Solve equations rational, polynomial, radical, absolute value, exponential, logarithmic, and trigonometric equations.</li><li>Solve polynomial, rational, and absolute value inequalities.</li></ul>
• SLO 3: EVALUATE, ANALYZE, COMPOSE, AND GRAPH FUNCTIONS.<ul><li>Synthesize connections between equations of functions and their graphs.</li><li>Apply transformations to the graphs of functions.</li><li>Recognize the relationship between a function and its inverse both graphically and algebraically.</li><li>Analyze and graph piecewise functions.</li><li>Compose functions and evaluate the domain of the resulting composition.</li></ul>
• SLO 4: SOLVE APPLICATION PROBLEMS REQUIRING EXPONENTIAL, LOGARITHMIC, AND TRIGONOMETRIC FUNCTIONS.<ul><li>Build exponential models for various applications occurring in nature, populations, and industry.</li><li>Use logarithmic formulas to investigate Richter Scale, decibels, lumens, and other sensory-based models.</li><li>Construct sinusoidal models for various applications.</li></ul>
• SLO 5: USE (RIGHT TRIANGLE) TRIGONOMETRY TO SOLVE EQUATIONS, PROVE IDENTITIES, GRAPH FUNCTIONS, SIMPLIFY EXPRESSIONS, AND WORK WITH APPLICATIONS.<ul><li>Evaluate trigonometric functions using right triangle trigonometry.</li><li>Simply expressions involving trigonometric functions using identities.</li><li>Prove trigonometric identities using the Pythagorean, Reciprocal, Ratio, Symmetry, Double-Angle, Sum and Difference of Angles, and Cofunction identities.</li><li>Solve equations and applications involving trigonometric functions.</li></ol>

Upon completion of this course, the student will be able to:

• SLO1: Evaluate limits of algebraic and transcendental functions, including limits at infinity.
• Use algebraic, graphical, and numerical approaches to evaluate limits; Use the epsilon-delta definition to prove limits.
• Identify indeterminate forms and utilize L’Hospital’s Rule.
• SLO2: Apply definition of continuity using limits to prove a function is continuous at a real number and discern the connection/difference between continuity and differentiability; Understand and identify singularities, including removable, jump, infinite, and oscillating.
• Determine whether a function is continuous at a real number from the left or from the right; Identify the interval(s) on which a function is continuous.
• SLO3: Compute derivatives using the limit definition of the derivative to determine where a function is differentiable or not at a point in its domain; apply differentiation rules to algebraic, trigonometric, exponential, logarithmic, hyperbolic functions, and their inverses.
• Compute derivatives by using implicit and logarithmic differentiation techniques.
• SLO4: Recognize and solve real world problems that require use of limits and/or derivatives.
• Without a graphing calculator, graph functions using the limits to find vertical, horizontal, and slant asymptotes, using the first derivative to find relative extreme values, using the second derivative to find concavity and inflection points; examine the connection between the graph of a function and the graph of its derivatives; generate equations of tangent/normal lines.
• Solve problems involving velocity, acceleration, related rates, optimization, linear approximation, and differentials.
• SLO5: Understand and apply the concept of the Riemann Sum to develop the formal definition of the definite integral and use the definition to evaluate definite integrals.
• Calculate definite integrals using the Fundamental Theorem of Calculus and appropriate substitution techniques.
• Interpret definite integral as "signed" area and use it to find the area under a curve; properties of the definite integral; approximate definite integrals with the midpoint rule.
• SLO6: Apply the definitions of limit, derivative, and integral to prove calculus theorems including the fundamental theorem of calculus (parts 1 and 2) and their applications.
• Apply theorems including the Intermediate Value Theorem, Rolle’s Theorem, and the Mean Value Theorem to derive related theorems and use them in applications.

Upon completion of this course, the student will be able to:

• SLO#1: Understand the concept of using the limit of a Riemann sum to find "signed" areas and volumes.
• Calculate the area between two curves in a plane region.
• Find the volume of a solid of revolution using the disk/washer method.
• Find the volume of a solid of revolution using the cylindrical shell method.
• Find the volume of a solid by using the method of cross sections by parallel planes.
• Analyze a problem and choose the best method to use to find an area or volume.
• SLO#2: Understand and appropriately apply techniques of integration.
• Use the method of integration by parts.
• Evaluate trigonometric integrals.
• Use the method of trigonometric substitution.
• Use partial fractions to integrate rational functions, including rationalizing substitutions.
• Approximate definite integrals using numerical methods including the trapezoidal rule and Simpson's rule.
• Understand what improper integrals are and evaluate them by writing them as a limit of a proper integral.
• Analyze a problem to choose the best method of integration.
• Develop a strategy for integration techniques.
• SLO#3: Understand other coordinate systems and how to apply calculus techniques to solve problems using them.
• Represent curves in parametric form and understand the calculus of parametric curves.
• Represent curves in polar form and understand the calculus of polar curves.
• Find areas, arc length, and surface area using Cartesian coordinates, polar coordinates and parametric equations.
• SLO#4: Apply the techniques of integral calculus to solve applied problems.
• Apply calculus to physics and engineering problems.
• Apply calculus to work, fluid force, and center of mass problems.
• Apply calculus to find the average value of functions.
• Apply calculus to solve separable differential equations and exponential growth and decay problems.
• SLO#5: Understand the theory of series.
• Understand the definition of a sequence and how to find their limits.
• Understand the definition of a series and determine whether they are convergent or divergent, including using partial sums, geometric, p-test, telescoping, and divergence test.
• Understand and apply both the basic comparison test and the limit comparison test.
• Understand and apply the integral test.
• Understand and apply the ratio and root tests.
• Understand and apply the alternating series test.
• Understand the difference between conditional and absolute convergence.
• Develop a general strategy for testing series for convergence.
• Identify power series and compute their radius and interval of convergence.
• Represent functions as power series including Taylor and Maclaurin series.
• Differentiate and integrate power series.

Upon completion of this course, the student will be able to:

• SLO 1: WORK WITH VECTORS AND GRAPHS IN BOTH TWO AND THREE DIMENSIONS
• perform operations on vectors in R2 and R3, including the dot and cross products, limits, derivatives, and integrals.
• graph lines, planes, cylinders, and quadric surfaces in R3.
• find the equations of lines (in R3) and planes.
• find the distances between a point and a line, a point and a plane, two planes, two skew lines, etc.
• compute the curvature at any point on a space curve along with the tangential and normal components of acceleration, the arc length, and the unit tangent and unit normal vectors.
• SLO 2: EVALUATE FUNCTIONS OF MORE THAN ONE VARIABLE AS WELL AS THEIR LIMITS, CONTINUITY, AND DERIVATIVES, AND APPLY THEM TO REAL WORLD PROBLEMS
• evaluate functions of more than one variable, find their domain and range, and sketch level curves and level surfaces.
• evaluate limits, prove limits using the epsilon-delta definition of a limit, show that limits do not exist using the "two path rule".
• examine the continuity for functions of more than one variable.
• evaluate partial derivatives and directional derivatives.
• calculate the gradient and use it to find equations of tangent planes to surfaces in R3.
• determine differentiability, calculate linearizations, differentials, and derivatives using the chain rule and apply them to real world problems.
• optimize a multivariate function on a space curve and a plane region, including both local extrema and absolute extrema, the latter including the use of Lagrange multipliers to solve constraint problems.
• SLO 3 EVALUATE MULTIPLE INTEGRALS AND APPLY THEM TO REAL WORLD PROBLEMS
• evaluate double and triple integrals using rectangular, polar, cylindrical, and spherical coordinate systems as well as change of variables using the Jacobian.
• calculate area, surface area, volume, mass, and center of mass using double and triple integrals.
• SLO 4: EVALUATE LINE INTEGRALS AND SURFACE INTEGRALS AND APPLY THEM TO THE APPROPRIATE REAL WORLD PROBLEMS
• evaluate line integrals using parametrization, the Fundamental Theorem of Line Integrals, Green's Theorem, and Stokes' Theorem and apply them to real world problems, including work.
• evaluate surface integrals using parametrization and the Divergence Theorem and apply them to real world problems, including flux.
• Find the divergence and curl of a vector field.

Upon completion of this course, the student will be able to:

• SLO 1: SOLVE SYSTEMS OF LINEAR EQUATIONS
• Solve systems of homogeneous and nonhomogeneous linear equations using Gaussian elimination, Gauss-Jordan elimination, and inverse matrices (in particular, the relationship between coefficient matrix invertibility and solutions to a system of linear equations).
• Solve vector equations.
• Examine vector algebra on R^n.
• Find a matrix representation of a linear transformation and solve matrix equations.
• Construct rigorous mathematical proofs involving linear equations, vector equations, vector algebra on R^n, and matrix equations.
• SLO 2: EXAMINE BASES
• Test for linear independence of a set of vectors.
• Test for the span of a set of vectors.
• Construct a change of basis.
• Construct rigorous mathematical proofs involving independence, span, and basis.
• SLO 3: EXAMINE MATRICES
• Determine whether a matrix is invertible and, if so, calculate its inverse.
• Construct factorizations of matrices, including LU factorization.
• Compute determinants of matrices.
• Examine special matrices: diagonal and triangular.
• Construct rigorous mathematical proofs involving matrices.
• SLO 4: EXAMINE VECTOR SPACES AND LINEAR TRANSFORMATIONS
• Test the linearity of a transformation from one vector space to another.
• Test whether a linear transformation is an isomorphism.
• Compute the Kernel and Range of a linear transformation.
• Test a subset of a vector space to determine if it is a subspace of said vector space.
• Examine the Null Space and Column Space of a matrix, including the Rank Nullity Theorem.
• Construct rigorous mathematical proofs involving vector spaces.
• SLO 5: EXAMINE EIGENSPACES AND ORTHOGONALITY
• Calculate dot product, norm of a vector, the angle between vectors in R^n, eigenvalues and eigenvectors and their use in applications.
• Diagonalize matrices.
• Construct orthogonal bases using the Gram-Schmidt process.
• Examine symmetric matrices and orthogonally diagonalize them.
• Construct rigorous mathematical proofs involving eigenspaces and orthogonality.

Upon completion of this course, the student will be able to:

• SLO 1: SOLVE FIRST ORDER DIFFERENTIAL EQUATIONS AND APPLY THEM TO REAL WORLD PROBLEMS
• Apply the theory of first order differential equations, including existence and uniqueness theorems for ordinary differential equations.
• Solve first order differential equations using separation of variables, exactness, linearity, and substitutions (including homogeneous and Bernoulli differential equations).
• Apply first order differential equations to real world problems, including exponential growth and decay, Newton's Law of Cooling, and mixture problems.
• SLO 2: SOLVE HIGHER ORDER DIFFERENTIAL EQUATIONS AND APPLY THEM TO REAL WORLD PROBLEMS
• Examine the theory of higher order differential equations, including the fundamental set of solutions, linear independence, and the Wronskian.
• Solve higher order homogeneous and nonhomogeneous linear differential equations with constant coefficients; annihilator operators and variation of parameters.
• Solve homogeneous and nonhomogeneous Cauchy-Euler differential equations.
• Solve homogeneous and nonhomogeneous linear ordinary differential equations with variable coefficients using power series solutions (including the theorem of Frobenius).
• Apply higher order differential equations to real world problems, including spring/mass problems and circuits.
• SLO 3: SOLVE INITIAL VALUE PROBLEMS USING LAPLACE TRANSFORMS AND APPLY THEM TO REAL WORLD PROBLEMS.
• Examine the theory of Laplace transform and its inverse.
• Solve initial value problems using Laplace Transforms, including the use of the translation theorems, the derivative of a Laplace transform, and convolution; the Laplace transform of a periodic function.
• Apply Laplace Transforms to real world problems.
• SLO 4: SOLVE SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS.
• Calculate eigenvalues and eigenvectors.
• Solve systems of linear homogeneous and nonhomogeneous differential equations using eigenvalues, eigenvectors, and inverse matrices.
• SLO 5: SOLVE INITIAL VALUE PROBLEMS USING NUMERICAL METHODS.
• Calculate numerical solutions to initial value problems.

Upon completion of this course, the student will be able to:

• SLO 1: EXAMINE METHODS OF PROOF
• Prove statements using axioms
• Prove statements using deductive reasoning
• Prove conditional statements
• Prove biconditional statements
• Prove statements using the contrapositive
• Prove statements using contradiction
• Prove statements using mathematical induction

Upon completion of this course, the student will be able to:

• SLO 1: EXAMINE THE PROPERTIES OF THE INTEGERS
• Examine divisibility
• Examine prime numbers
• Calculate the greatest common divisor
• Examine the fundamental theorem of arithmetic
• Prove theorems involving the integers
• SLO 2: EXAMINE DIOPHANTINE EQUATIONS
• Examine the Euclidean algorithm
• Solve linear Diophantine equations
• Prove theorems involving Diophantine equations
• SLO 3: EXAMINE LINEAR CONGRUENCES
• Examine modular arithmetic
• Examine the properties of congruences
• Solve congruence equations
• Prove theorems involving linear congruences
• SLO 4: EXAMINE CRYPTOLOGY
• Examine the theory of cryptology
• Examine encoding messages
• Examine decoding messages
• Prove theorems involving cryptology

Upon completion of this course, the student will be able to:

• SLO #1: Actively engage in intellectual inquiry beyond that required in order to pass a course of study (College Wide Learning Outcome – Area 4).
• Discuss and outline a proposal of study (that can be accomplished within one semester term) with a supervising instructor qualified within the discipline.
• Design an independent study (to be completed individually or by collaboration of a small group) to foster special knowledge, skills, and experience that are not available in any one regularly scheduled course.
• Use information resources to gather discipline-specific information.
• SLO #2: Utilize modes of analysis and critical thinking to apply theoretical perspectives and/or concepts in the major discipline of study to significant problems and/or educational activities (College Wide Learning Outcome – Area 3).
• Analyze and apply the knowledge, skills and experience that are involved in the independent study to theoretical perspectives and/or concepts in the major discipline of study.
• Explain the importance of the major discipline of study in the broader picture of society.
• SLO #3: Communicate a complex understanding of content matter of the major discipline of study (College Wide Outcome – Area 3).
• Demonstrate competence in the skills essential to mastery of the major discipline of study that are necessary to accomplish the independent study.
• SLO #4: Identify personal goals and pursue these goals effectively (College Wide Outcome – Area 4).
• Utilize skills from the “academic tool kit” including time management, study skills, etc., to accomplish the independent study within one semester term.

Upon completion of this course, the student will be able to:

• SLO 1: Use mathematics support skills to analyze and investigate properties of functions;<ul><li>Understand foundational elementary concepts and definitions of functions.</li><li>Perform fundamental evaluation of functions.</li></ul>
• SLO 2: Use mathematics support skills to synthesize results from the graphs and/or equations of functions;<ul><li>Interpret basic information from the graph of a function.</li><li>Identify qualities of a graph that are cornerstones of what makes it representative of a function.</li></ul>
• SLO 3: Use mathematics support skills to solve and apply equations;<ul><li>Understand, and be able to use, the core techniques to solving rational, linear, absolute value, polynomial, exponential, and logarithmic equations.</li><li>Interpret key phrases within a real-world problem linked to functions and operations.</li></ul>
• SLO 4: Use mathematics support skills to solve linear and nonlinear systems of equations and inequalities;<ul><li>Understand the basic building blocks of consistent and inconsistent systems, and be able to identify such systems graphically.</li></ul>
• SLO 5: Use mathematics support skills to apply functions and other algebraic techniques to model real-world applications;
• SLO 6: Use support mathematics skills to recognize the relationship between functions and their inverses graphically and algebraically;<ul><li>Create an inverse function given linear, rational, radical, exponential, and logarithmic functions.</li></ul>
• SLO 7: Use support mathematics skills to apply transformations to the graphs of functions.<ul><li>Perform basic transformation techniques on graphs of functions.</li></ul>

Upon completion of this course, the student will be able to:

• SLO 1: SIMPLIFY EXPRESSIONS NECESSARY TO BE SUCCESSFUL IN CALCULUS I. <ul><li>Simplify expressions with negative rational exponents using laws of exponents.</li><li>Simplify compound rational expressions.</li><li>Simplify logarithmic expressions using laws of logarithms.</li></ul>
• SLO 2: SOLVE EQUATIONS NECESSARY TO BE SUCCESSFUL IN CALCULUS I. <ul><li>Solve exponential, logarithmic, rational, radical, absolute value, and polynomial equations.</li><li>Use Factor Theorem to extract roots.</li></ul>
• SLO 3: SOLVE INEQUALITIES NECESSARY TO BE SUCCESSFUL IN CALCULUS I. <ul><li>Solve absolute value inequalities.</li><li>Solve nonlinear inequalities, including polynomial, exponential, logarithmic, rational, and radical inequalities.</li></ul>
• SLO 4: EVALUATE AND GRAPH FUNCTIONS NECESSARY TO BE SUCCESSFUL IN CALCULUS I. <ul><li>Analyze absolute value of a function |f(x)|.</li><li>Determine the domain and range of a function.</li><li>Evaluate a function at an expression.</li><li>Evaluate piecewise, basic exponential and logarithmic functions.</li><li>Evaluate composition of functions.</li><li>Determine domain restrictions for functions to be invertible, and find their inverse.</li><li>Analyze polynomial, rational, radical, and absolute value functions, including their graphs and transformations.</li></ul>
• SLO 5: APPLY METHODS FROM GEOMETRY AND TRIGONOMETRY NECESSARY TO BE SUCCESSFUL IN CALCULUS I. <ul><li>Use similar triangles to solve ratio problems.</li><li>Use unit circle trigonometry to find the six trigonometric values at special angles.</li><li>Use right triangle trigonometry to solve angles or sides, and to solve word problems.</li><li>Solve trigonometric equations.</li><li>Use trigonometric identities, including cofunction, reciprocal, ratio, Pythagorean, symmetry, sum and difference, and double-angle identities, to evaluate an expression or solve an equation.</li><li>Graph all six trigonometric functions and their transformations.</li><li>Evaluate inverse trigonometric expressions.</li><li>Graph inverse trigonometric functions.</li><li>Use Law of Sines and Law of Cosines to solve acute or obtuse triangles, and apply them to word problems.</li><li>Find equations of conic sections in standard form and graph them.</li></ul>
• SLO 6: USE SUMS AND SUMMATION PROPERTIES NECESSARY TO BE SUCCESSFUL IN CALCULUS I. <ul><li>Use sigma notation and evaluate nth partial sums.</li><li>Apply summation properties to evaluate sums.</li><li>Evaluate basic sums involving i,i^2, and i^3.</li><li>Use Pascal’s Triangle to expand powers of binomials.</li></ul>
• SLO 7: APPLY BASIC LOGIC NECESSARY TO BE SUCCESSFUL IN CALCULUS I. <ul><li>Identify the components of a conditional statement.</li><li>Identify the converse and contrapositive of a conditional statement and their significance.</li><li>Prove mathematical facts using algebraic manipulations, trigonometric identities, direct proof, and indirect proof.</li><li>Perform proof by mathematical induction.</li></ul>

Upon completion of this course, the student will be able to:

• SLO 1: APPLY LEARNING STRATEGIES TO ACHIEVE SUCCESS IN COLLEGE ALGEBRA FOR CALCULUS.
• Objective 1a: use mathematics support skills to solve equations and inequalities and manipulate expressions.
• Objective 1b: use mathematics support skills to solve systems of equations and inequalities.
• Objective 1c: use mathematics support skills to demonstrate a deep understanding of functions and their properties.

Upon completion of this course, the student will be able to:

• SLO 1: APPLY LEARNING STRATEGIES TO ACHIEVE SUCCESS IN TRIGONOMETRY FOR CALCULUS
• Objective 1a: recall the methods from arithmetic necessary to be successful in Trigonometry for Calculus
• Objective 1b: review the methods from algebra necessary to be successful in Trigonometry for Calculus
• Objective 1c: apply learning strategies to achieve success in Trigonometry for Calculus
• Objective 1d: demonstrate an understanding of the methods from geometry necessary to be successful in Trigonometry for Calculus

Upon completion of this course, the student will be able to:

• SLO 1: USING COMPUTATIONAL SKILLS AND NUMBER SENSE, RECOGNIZE THE ORDER OF OPERATIONS AND PROPERTIES OF REAL NUMBERS.<ul><li>Review the Order of Operations and the properties of numbers, as needed.</li></ul>
• SLO 2: FACTOR BINOMIALS, TRINOMIALS, AND POLYNOMIALS.<ul><li>Factor binomials using the Difference of Squares and the Sum and Difference of Cubes formulas.</li><li>Factor polynomials using the GCF and grouping.</li><li>Factor trinomials with unit and non-unit lead coefficients.</li></ul>
• SLO 3: IDENTIFY AND ANALYZE LINEAR BEHAVIOR, MODELS, AND GRAPHS OF LINEAR EQUATIONS.<ul><li>Write the equation of a line in both point-slope and slope-intercept forms.</li><li>State the meaning of the slope in a linear model.</li><li>Graph linear functions.</li></ul>
• SLO 4: IDENTIFY, SIMPLIFY, EVALUATE, AND GRAPH QUADRATIC FUNCTIONS USING THE PROPERTIES OF QUADRATIC FUNCTIONS AND TRANSFORMATIONS.<ul><li>Graph quadratic functions.</li><li>State the vertex of a quadratic function.</li></ul>
• SLO 5: SIMPLIFY POLYNOMIAL, RADICAL, AND RATIONAL EXPRESSIONS, AS WELL AS EXPRESSIONS REQUIRING THE LAWS OF EXPONENTS.<ul><li>Simplify polynomial, radical, and rational expressions, including sums, differences, products, and quotients.</li><li>Review and extensively use the Laws of Exponents.</li></ul>
• SLO 6: SOLVE POLYNOMIAL, RADICAL, AND RATIONAL EQUATIONS.<ul><li>Solve equations involving polynomial, radical, and rational functions.</li></ul>

Upon completion of this course, the student will be able to:

• SLO 1: READ, EVALUATE AND CONVERSE USING BASIC STATISTICAL TERMINOLOGY.
• Recognize a sample as a subset of a population, read and identify the description of samples and populations as presented in statistical situations.
• Summarize and symbolize information using statistical notation.
• Converse with classmates using statistical terminology.
• SLO 2: PERFORM AND INTERPRET COMPUTATIONAL MATHEMATICS USED IN STATISTICS AND PROBABILITY.
• Use and interpret fractions, decimals and percents, including use of decimal place values and rounding.
• Simplify linear expressions, solve linear equations and rewrite literal equations (formulas) to solve for a particular variable.
• Translate inequality statements, solve linear inequalities and demonstrate the solution on a number line.
• Translate applied situations (english) to statistical knowns and unknowns and apply these to evaluate statistical formulas using the order of operations.
• SLO 3: CREATE AND INTERPRET STATISTICAL GRAPHS AND TABULAR DISPLAYS OF DATA.
• Create and interpret frequency tables, relative frequency tables, bar graphs, histograms, stem and leaf displays, boxplots and scatterplots.
• SLO 4: APPLY PROBABILITY, SET THEORY AND ORGANIZATIONAL TOOLS SUCH AS VENN DIAGRAMS AND 2-WAY TABLES TO QUANTIFY THE LIKELIHOOD OF CHANCE OUTCOMES.
• Compute and interpret relative frequency observational probability and classical sample space probabilities.
• Compute and interpret the probabilities of an event, the complement of an event, and the union and intersection of events.
• Use Venn Diagrams and 2-way tables to compute and interpret the probabilities of and event, the complement of an event, unions and intersections of events, and conditional probabilities.
• Compute and interpret the area under a histogram to determine probabilities.
• Compute and interpret the area under continuous curves using symmetry or partial sums to determine probabilities.
• SLO 5: CREATE AND INTERPRET GRAPHS OF LINEAR AND EXPONENTIAL FUNCTIONS AND USE THEM TO MODEL BIVARIATE DATA.
• Sketch the graphs of linear and exponential functions.
• Find the equations of linear and exponential functions given two points on the line or curve.
• Use technology to find the equations of linear and exponential functions given a data set.
• Interpret the parameters of the linear and exponential models and explain how these parameters describe relationships in the data.
• Use linear and exponential models to compute predictions and make comparisons between models.

Upon completion of this course, the student will be able to:

• Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data
• Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics.
• Describe and apply probability concepts and distributions.
• Demonstrate an understanding of, and ability to use, basic ideas of statistical processes, including hypothesis tests and confidence interval estimation.
• Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results.
• Evaluate ethical issues in statistical practice.
• Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data. <ul><li>Recognize data types and data sources: develop basic statistical terminology including population parameters and sample statistics; identify common sampling methods used for obtaining data and identify advantages and disadvantages of each; recognize bias in sampling; compare principles of good experimental design. </ul>
• Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics. <ul><li>Organize and display data appropriately by preparing tables and graphs.</li><li>Analyze data by computing measures of central tendency, measures of dispersion, and measures of position.</li><li>Analyze bivariate data for linear trends using the least-squares regression model and the correlation coefficient.</li></ul>
• Describe and apply probability concepts and distributions <ul><li>Compute probabilities using sample spaces, the addition and multiplication rules, conditional probability, and complements.</li><li>Develop and apply probability distributions for discrete random variables; compute probabilities and expected value.</li><li>Analyze both discrete and continuous probability distributions by considering areas under the graph of a function or a histogram.</li><li>Use the normal and binomial probability distributions to compute probabilities.</li></ul>
• Demonstrate an understanding of, and ability to use, basic ideas of statistical processes, including hypothesis tests and confidence interval estimation. <ul><li>Create and interpret confidence interval estimates for population mean and population proportion based on appropriate probability models. </li><li>Select the appropriate hypothesis test, perform the necessary computations and comparisons to test hypotheses about one population mean or one population proportion and explain the conclusion of the test.</li><li>Create and interpret confidence interval estimates for the difference in two population means (independent and dependent sampling) or two population proportions</li><li>Select the appropriate hypothesis test, perform the necessary computations and comparisons to test hypotheses about two-population means (independent and dependent sampling), more than two population means, and two or more population proportions and explain the conclusion of the test. </li><li>Test significance of correlation and make predictions based on linear trends using the least-squares regression model.</li></ul>
• Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results. <ul><li>Use statistical software or graphing calculator to organize and graphically display data</li><li>Use statistical software or graphing calculator to calculate single-variable and two-variable statistics.</li><li>Use statistical software or graphing calculator to compute probabilities for discrete and continuous random variables, including binomial random variables and normally distributed random variables. </li><li>Use statistical software or graphing calculator to graph bivariate data, compute the correlation coefficient and linear regressions equation.</li><li>Use statistical software or graphing calculator to construct confidence intervals for population parameters and the difference between parameters.</li><li>Use statistical software or graphing calculator to conduct hypothesis tests by generating the P-value.</li></ul>
• Use appropriate statistical techniques to analyze and interpret applications of data <ul><li>Analyze the use of qualitative and quantitative data as it relates to business, economics, social sciences, psychology, life science, health science and education.</li><li>Use appropriate statistical techniques to address applications in a variety of disciplines including business, economics, social sciences, psychology, life science, health science, and education.</li></ul>

Upon completion of this course, the student will be able to:

• Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data.
• Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics.
• Describe and apply probability concepts and distributions.
• Demonstrate an understanding of, and ability to use, basic ideas of statistical processes, including hypothesis tests and confidence interval estimation.
• Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results.
• Evaluate ethical issues in statistical practice.
• Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data.<br> • Recognize data types and data sources: develop basic statistical terminology including population parameters and sample statistics; identify common sampling methods used for obtaining data and identify advantages and disadvantages of each; recognize bias in sampling; compare principles of good experimental design.
• Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics.<br> • Organize and display data appropriately by preparing tables and graphs.<br> • Analyze data by computing measures of central tendency, measures of dispersion, and measures of position.<br> • Analyze bivariate data for linear trends using the least-squares regression model and the correlation coefficient.<br>
• Describe and apply probability concepts and distributions. • Compute probabilities using sample spaces, the addition and multiplication rules, conditional probability, and complements. <br> • Develop and apply probability distributions for discrete random variables; compute probabilities and expected value.<br> • Analyze both discrete and continuous probability distributions by considering areas under the graph of a function or a histogram.<br> • Use the normal and binomial probability distributions to compute probabilities
• Demonstrate an understanding of, and ability to use, basic ideas of statistical processes, including hypothesis tests and confidence interval estimation.<br> • Create and interpret confidence interval estimates for population mean and population proportion based on appropriate probability models.<br> • Select the appropriate hypothesis test, perform the necessary computations and comparisons to test hypotheses about one population mean or one population proportion and explain the conclusion of the test.<br> • Create and interpret confidence interval estimates for the difference in two population means (independent and dependent sampling) or two population proportions.<br> • Select the appropriate hypothesis test, perform the necessary computations and comparisons to test hypotheses about two-population means (independent and dependent sampling), more than two population means, and two or more population proportions and explain the conclusion of the test. <br> • Test significance of correlation and make predictions based on linear trends using the least-squares regression model.
• Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results. • Use statistical software or graphing calculator to organize and graphically display data. • Use statistical software or graphing calculator to calculate single-variable and two-variable statistics.<br> • Use statistical software or graphing calculator to compute probabilities for discrete and continuous random variables, including binomial random variables and normally distributed random variables.<br> • Use statistical software or graphing calculator to graph bivariate data, compute the correlation coefficient and linear regressions equation.<br> • Use statistical software or graphing calculator to construct confidence intervals for population parameters and the difference between parameters.<br> • Use statistical software or graphing calculator to conduct hypothesis tests by generating the P-value.
• Use appropriate statistical techniques to analyze and interpret applications of data. • Analyze the use of qualitative and quantitative data as it relates to business, economics, social sciences, psychology, life science, health science and education.<br> • Use appropriate statistical techniques to address applications in a variety of disciplines including business, economics, social sciences, psychology, life science, health science, and education.
• In addition, as a course in the Honors Program, this course should support the following additional learning objectives:<br><br> Express ideas clearly in well-organized written messages.<br> • Express ideas clearly and completely in a variety of written formats.<br> • Utilize correct and appropriate conventions of mechanics, usage, and style in written communication. • Comprehend main ideas and reasonably interpret written information.<br> • Compose and apply properly documented sources of information.<br>
• In addition, as a course in the Honors Program, this course should support the following additional learning objectives:<br><br> Utilize modes of analysis and critical thinking in a discipline of study as applied to significant issues and/or problems.<br> • Analyze reasoning processes to evaluate issues, value judgments or conclusions that determine the quality, validity, and/or reliability of information.<br> • Construct an accurate and/or logical interpretation of reasoning while applying a framework of analytic concepts.<br> • Communicate a complex understanding of content matter of a major discipline of study.<br> • Explain the importance of the major discipline of study in the broader picture of society.
• In addition, as a course in the Honors Program, this course should support the following additional learning objectives:<br><br> Actively engage in intellectual inquiry beyond that required in order to pass a course of study.<br> • Apply information and resources necessary to develop academically and personally.<br> • Utilize skills from one’s “academic tool kit” including time management, study skills, etc.<br>
• In addition, as a course in the Honors Program, this course should support the following additional learning objectives:<br><br> Recognize the ethical dimensions of decisions and actions.<br> • Demonstrate the ability to engage in ethical reasoning necessary to exercise responsibility as an ethical individual, professional, local, and global citizen.
• In addition, as a course in the Honors Program, this course should support the following additional learning objectives:<br><br> Articulate an awareness of a variety of perspectives within a discipline and the relevance of these perspectives to one’s own life.

Upon completion of this course, the student will be able to:

• SLO #1: Actively engage in intellectual inquiry beyond that required in order to pass a course of study (College Wide Learning Outcome – Area 4).
• Discuss and outline a proposal of study (that can be accomplished within one semester term) with a supervising instructor qualified within the discipline.
• Design an independent study (to be completed individually or by collaboration of a small group) to foster special knowledge, skills, and experience that are not available in any one regularly scheduled course.
• Use information resources to gather discipline-specific information.
• SLO #2: Utilize modes of analysis and critical thinking to apply theoretical perspectives and/or concepts in the major discipline of study to significant problems and/or educational activities (College Wide Learning Outcome – Area 3).
• Analyze and apply the knowledge, skills and experience that are involved in the independent study to theoretical perspectives and/or concepts in the major discipline of study.
• Explain the importance of the major discipline of study in the broader picture of society.
• SLO #3: Communicate a complex understanding of content matter of the major discipline of study (College Wide Outcome – Area 3).
• Demonstrate competence in the skills essential to mastery of the major discipline of study that are necessary to accomplish the independent study.
• SLO #4: Identify personal goals and pursue these goals effectively (College Wide Outcome – Area 4).
• Utilize skills from the “academic tool kit” including time management, study skills, etc., to accomplish the independent study within one semester term.