# Mathematics (MTH) CPSO

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Course numbers with the # symbol included (e.g. #400) have not been taught in the last 3 years.

**MTH 402 - Math for Our World **

**Credits:** 4

This course takes an integrated approach to the study of mathematics, combining mathematical concepts with applications in the real world. It addresses topics in mathematics necessary in a college education, providing the reasoning strategies needed for mathematical problem solving in the workplace, the media, and everyday life. The course serves as the foundation for higher-level math courses and provides the quantitative skills necessary to be adequately prepared for coursework in other academic areas. The overarching goal is to learn to interpret quantitative and statistical information that we encounter daily. Students will understand how real-world problems can be analyzed using the power and rigor of mathematical and statistical models. Topics include: problem solving, math of finance, geometry, basic probability, and beginning statistical concepts with an emphasis on real world applications and interpreting information. The use of Excel will be incorporated into the topics of this course. Acceptable scores on Accuplacer Arithmetic and Elementary Algebra Accuplacer Classic or Next Generation Accuplacer assessments; or approved exemption based on previous high school transcripts: a grade of C or better in both Algebra and Geometry taken within the last five years; or SAT Math score of 500+ or ACT Math score of 18+ taken within five years of registration; or successful completion of the ALEKS Program Math Tutorial as determined by the college's math faculty required. Accuplacer or ALEKS assessments should be completed within five years of registering for course.

**Attributes:** Mathematics (Gen Ed); Quantitative Reasoning(Disc)

**Prerequisite(s):** (Classic Arithmetic Accuplacer with a score of 080 and CL Elem Algebra - Accuplacer with a score of 036) or (Arithmetic Accuplacer-Next Gen with a score of 263 and Quant,Alg,Stats Accp-Next Gen with a score of 237) or C MATH 405/or taken elsewhere with a score of WAIV or SAT Math with a score of 500 or ACT Reading with a score of 18 or GSC Math Workshop Completed with a score of WAIV.

**Equivalent(s):** MATH 502G

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Select appropriate approaches and methods, such as logic, set theory, estimation, and proportional reasoning, to solve problems.
- Assess reasonableness of answers, identify alternatives, and select the best solutions.
- Extract quantitative data for a given situation from different types of mathematical models.
- Translate word problems into their symbolic representations.
- Use mathematical modeling to solve application problems symbolically, numerically, and graphically.
- Use probability to make inferences and informed decisions.
- Organize data and make predictions about real-world situations using statistical methods and models.

**MTH 504 - Statistics **

**Credits:** 4

This course addresses introductory statistical concepts, methods, and procedures important for making well-informed decisions in real world settings. It provides students with both theoretical principles and practical skills in statistics. Topics include an overview of descriptive and inferential statistics, specifically sampling, measurements of central tendency and dispersion, frequency distributions, graphing techniques, probability theory, hypothesis testing, normal distribution, regression and correlation, t-tests, and analysis of variance. An acceptable score on the Classic or Next Generation Accuplacer arithmetic and elementary algebra assessment. Accuplacer assessments should be completed within five years of registering for course. NOTE: Excel proficiency is expected prior to enrollment in this course.

**Attributes:** Mathematics (Gen Ed); Quantitative Reasoning(Disc)

**Prerequisite(s):** MTH 402 with a minimum grade of D- or MATH 502G with a minimum grade of D-.

**Equivalent(s):** MATH 504G

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Recognize the use of best practices in design of experiments including sampling procedures, and data collection methods in real world situations.
- Interpret basic data visualization techniques, such as frequency distributions, bar charts, histograms, boxplots, scatterplots, and time series.
- Solve basic problems based on and describe the intended use for measurements of central tendency and dispersion including means, medians and modes; and variance, standard deviations, z-scores, and percentiles.
- Apply basic probability rules and characteristics of discrete and continuous probability distributions to solve and interpret real-world problems.
- Explain concepts used to arrive at a hypothesis for real-world situations and test its validity.
- Discuss current ethical standards that pertain to the use of statistical methods, data, and research results in modern day.

**MTH 510 - Pre-Calculus **

**Credits:** 4

This course is intended as a bridge course between algebra and calculus. The course focuses on strengthening the student's mathematical problem solving skills and developing a firm understanding of functions, their graphical representation, their behavior, and their use to model real-life situations. Various classes of functions will be highlighted: polynomials, rational, exponential, logarithmic, and trigonometric. Topics may also include: algebraic concepts, real number system, systems of equations and inequalities, complex numbers, and polar coordinates. An acceptable score on the Classic or Next Generation Accuplacer assessment(s) is accepted prior to taking this course. Accuplacer assessments should be completed within five years of registering for course. A graphing calculator is required.

**Attributes:** Mathematics (Gen Ed); Quantitative Reasoning(Disc)

**Prerequisite(s):** MTH 402 with a minimum grade of D- or MATH 502G with a minimum grade of D-.

**Equivalent(s):** MATH 510G

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Define a function verbally, numerically, visually, and algebraically as well as define and find its domain and range.
- Perform operations on functions such as: addition, multiplication, division, composition, and finding inverse functions.
- Graph and specify the algebraic characteristics of polynomial, rational, radical, exponential, logarithmic, and trigonometric functions, both by hand and by graphing calculators.
- Identify the characteristics of the conic sections, both graphically and algebraically.
- Manipulate and evaluate algebraic, exponential, logarithmic and trigonometric functions.
- Employ mathematical modeling techniques to solve problems using polynomial, rational, radical, exponential, logarithmic, and trigonometric functions.
- Solve problems involving the intermediate value theorem, the division algorithm of polynomials, the remainder theorem, the factor theorem, and zeros of a polynomial.
- Solve problems involving systems of equations and inequalities in two unknowns.
- Interpret and define the six trigonometric functions, in terms of both right triangles and the unit circle.
- Graph trigonometric and inverse trigonometric functions, with and without the aid of a graphing calculator.
- Verify and apply trigonometric identities and formulas and apply them to solve trigonometric equations and word problems.
- Gain skill in the use of polar coordinates, specifically perform conversions between polar and Cartesian coordinates and sketch graphs of polar curves in both Cartesian and polar coordinates both by hand and using technology.

**MTH 544 - Special Topics: Lower Level **

**Credits:** 1-4

A study of current and variable topic in mathematics. Course content will change from term to term.

**Repeat Rule:** May be repeated up to unlimited times.

**Equivalent(s):** MATH 544G

**Grade Mode:** Letter Grading

**MTH 701 - Probability and Statistics **

**Credits:** 4

In this course students study topics in data analysis including: descriptive and inferential statistics, probability, odds and fair games, probability distributions, normal distributions, and estimation. Among the topics are numerical and graphical summaries for one and two variables, linear regression and correlation, confidence intervals and tests concerning means, sampling and experimentation, basic probability, confidence intervals, hypothesis testing, sampling distributions, two-sample t-tests for means, chi-squared tests, regress and correlation, and possible other topics. A standards statistical software package is used throughout the course to support the course format that includes: hands-on activities, computer-based simulations, creating and implementing student developed investigations, and actual secondary and middle school mathematics classroom activities. Throughout the course students are given opportunities to relate the mathematical concepts studied in this course to the mathematical concepts they will be teaching.

**Prerequisite(s):** MTH 402 with a minimum grade of D- or MATH 502G with a minimum grade of D-.

**Equivalent(s):** MATH 603G

**Mutual Exclusion:** No credit for students who have taken MATH 439, MATH 539, MATH 623.

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Design investigations, collect data, display data in a variety of ways, and interpret data representations including bivariate data, conditional probability, and geometric probability.
- Use appropriate methods to estimate population characteristics, test conjectured relationships among variables, and analyze data.
- Use appropriate statistical methods and technology to analyze data and describe shape, spread, and center.
- Use both descriptive statistics to analyze data, make predictions, test hypotheses, and make decisions.
- Draw conclusions involving uncertainty by using hands-on and computer-based simulations.
- Apply probability concepts in identifying odds, fair games, mathematical expectation, and invalid conclusions.
- Judge the validity of a statistical argument, including evaluating the sample from which the statistics were developed and identify misuses of statistics.
- Demonstrate knowledge of the historical development of probability and statistics.
- Determine and compare experimental, theoretical, and conditional probabilities.
- Use statistical models to explore the connections between statistics and probability including correlation, regression, and analysis of variance. (Standard ~ 612.18 NH (7.a-j) ; Standard ~ 612017 NH (7.a-j))

**MTH 702 - Mathematical Proof **

**Credits:** 4

This course introduces students to the language and methods used to create and write mathematical proofs and solve problems. Methods of proof will include: direct, contrapositive, contradiction, and induction. Methods of problem solving will be based on Polya's four steps for problem solving. Students will learn about and utilize the many functions of proof including: verification, explanation, communication, discovery, justification, and inquiry. The course will also explore the relationship between problem solving and the process of proving. Students will explore fundamental abstract concepts in mathematics chosen from the following areas: functions and relations, set theory, number theory, and logic, Euclidian and non-Euclidian geometry, algebra, mathematical reasoning, proof, and problem solving. Connections to middle and secondary school mathematics.

**Prerequisite(s):** MTH 510 with a minimum grade of D- or MATH 510G with a minimum grade of D-.

**Equivalent(s):** MATH 600G

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Use problem solving to investigate and understand increasingly complex mathematical content, including, but not limited to the ability to use problem-solving to develop ones own mathematical knowledge, reflect upon solutions and the problem-solving process, as well as refine strategies as needed.
- Use mathematical proof, including, but not limited to, the ability to develop and evaluate mathematical conjectures, to construct and evaluate proofs and logical arguments to verify conjectures, to select and use various types of reasoning and methods of proof, and to demonstrate the capacity to articulate an understanding of how reasoning and proof are integral components of mathematics.

**MTH 703 - Number Systems **

**Credits:** 4

This course examines the structure and properties of mathematics while focusing on the development of mental mathematics strategies and problem solving skills. Topics include sets, functions, applications of rational numbers, integers, fractions, decimals, percentages, and number theory. Appropriate grade level techniques are utilized to investigate algorithms, probability and statistics, counting techniques, scientific notation, complex numbers, exponents, geometry, and measurement. Students will also investigate ratios, proportion, data analysis, patterns, and the connections to algebra and geometry topics in the context of the 5-12 grades mathematics curriculum.

**Prerequisite(s):** MTH 510 with a minimum grade of D- or MATH 510G with a minimum grade of D-.

**Equivalent(s):** MATH 601G

**Mutual Exclusion:** No credit for students who have taken MATH 621.

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Demonstrate a capacity to use models to explore certain relationships, including magnitude, among fractions, decimals, percents, rations, and proportions.
- Demonstrate knowledge of the historical development of number and number systems.
- Apply, explain, and justify concepts in number and number theory.
- Demonstrate computational proficiency and fluency, including the use of a variety of algorithms, estimation strategies, and mental mathematics techniques to judge the reasonableness of answers or approximate solutions.
- Demonstrate knowledge of concepts and applications of limits and infinity.
- Demonstrate a capacity to apply the concepts of proportional reasoning.
- Demonstrate a capacity to make sense of large and small numbers and use scientific notation in mathematical and scientific modeling.

**MTH 704 - Geometric Structures **

**Credits:** 4

This course will examine concepts in Euclidean and non-Euclidean geometries. Course topics include area and volume, two- and three-dimensional perspective, congruence and similarity, properties of and relationships among geometric shapes and structures. Students will investigate graphing, vectors, motion, and symmetry. Students engage in course concepts through proofs, problem solving, dynamic geometric software, and through activities used in secondary and middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.

**Prerequisite(s):** MTH 510 with a minimum grade of D- or MATH 510G with a minimum grade of D-.

**Equivalent(s):** MATH 602G

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Build and manipulate representations of 2 and 3 dimensional objects and perceive an object from different perspectives.
- Analyze properties of and relationships among geometric shapes and structures.
- Apply transformations with connections to congruency and similarity.
- Demonstrate knowledge of non-Euclidean geometries and the historical development of the various geometries.
- Connect the ideas of algebra and geometry through the use of coordinate geometry, graphing, vectors, and motion geometry.
- Recognize measurement attributes and their effect on the choice of appropriate tools and units.
- Apply strategies, techniques, tools and formulas to determine measurements and their application in a variety of contexts.
- Demonstrate knowledge of the historical development of measurement and measurement systems.
- Employ estimation as a way of understanding measurement processes and units.
- Complete error analysis through determination of the reliability of numbers obtained from measurement.
- Understand and apply measurement conversion strategies.
- Apply geometric ideas and tools relating to the Pythagorean theorem, similar triangles, and trigonometry to solve problems.
- Use constructions, models, and dynamic geometric software to explore geometric relationships.
- Derive and explain formulas found in Euclidean geometry.
- Construct proofs using the axioms of Euclidean and non-Euclidean geometries.

**MTH 705 - Calculus I **

**Credits:** 4

This course is the first semester of a calculus sequence dealing with applications and modeling of the differential and integral calculus. The course focuses on functions and their graphs, limits, continuity, differentiation, integration, the derivative and its uses in optimization and mathematical modeling, as well as the Fundamental Theorem. Throughout the course students are given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching. Graphing calculators are used throughout the course to explore and represent concepts.

**Prerequisite(s):** MTH 510 with a minimum grade of D- or MATH 510G with a minimum grade of D-.

**Equivalent(s):** MATH 606G

**Mutual Exclusion:** No credit for students who have taken MATH 425, MATH 426.

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Use mathematical modeling and the concepts of calculus to represent and solve problems from real-world contexts.
- Use technology to explore and represent fundamental concepts of calculus.
- Demonstrate knowledge of the historical development of calculus.
- Understand and describe the connection of calculus to middle and high school mathematics topics.
- Demonstrate a conceptual understanding of and procedural facility with basic calculus concepts including limits, continuity, differentiation, and integration. (Standard ~ 612.18 NH (8.a-e) ; Standard ~ 612.17 NH (8.a-e).

**MTH 706 - History of Mathematics **

**Credits:** 4

This course addresses the historical development of major themes in mathematics, including calculation, numbers, geometry, algebra, infinity, and formalism in various civilizations ranging from the antiquity of Babylonia and Egypt through classical Greece, the Middle and Far East, and on to modern Europe. The course emphasizes how earlier civilizations influenced or failed to influence later ones and how the concepts evolved in these various civilizations.

**Prerequisite(s):** MTH 705 with a minimum grade of D- or MATH 606G with a minimum grade of D-.

**Equivalent(s):** MATH 608G

**Mutual Exclusion:** No credit for students who have taken MATH 790.

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Develop and strengthen their conceptual knowledge of arithmetic, algebra, geometry, trigonometry and calculus through the study of why and how these concepts developed.
- Analyze how the development of mathematical concepts in different cultures influenced the development of those cultures and our present culture.
- Explore the influence of the development of mathematical concepts on other disciplines.
- Follow the development of mathematics from early number systems to the invention of calculus.
- Research historical questions and applications and present conclusions to others.

**MTH 707 - Calculus II **

**Credits:** 4

This course is the second semester of a calculus sequence dealing with applications of differential and multivariable calculus. Topics include the calculus of transcendental functions, applications of integration, some differential equations, sequences and series, differentiation and integration of trigonometric functions multidimensional calculus with applications, and an introduction to multivariable calculus. Throughout the course students are given opportunities to relate the mathematical concepts studies to the mathematical concepts they will be teaching. Graphing calculators are used throughout the course to explore and represent concepts.

**Prerequisite(s):** MTH 705 with a minimum grade of D- or MATH 606G with a minimum grade of D-.

**Equivalent(s):** MATH 607G

**Mutual Exclusion:** No credit for students who have taken MATH 426, MATH 527, MATH 528.

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Demonstrate an understanding of basic concepts of multivariable calculus. (Standard ~ 612.18 NH (8.f)

**MTH 708 - Discrete Mathematics **

**Credits:** 4

This course is designed to introduce students to discrete and abstract mathematical topics. Topics include propositional and predicate logic; elementary set theory; introduction to proof techniques including mathematical induction; sets, relations, functions, and relations; recurrence relations, graph theory, as well as the properties of groups, rings, and fields. Students study number systems, mathematical induction, algorithms and complex number systems, matrix manipulation, combinatorics, graph theory, and finite differences. Course activities are based on secondary and middle school mathematics curricula. This course considers the basic objects of mathematics through real-world examples and the methods used to elucidate their properties.

**Prerequisite(s):** MTH 705 with a minimum grade of D- or MATH 606G with a minimum grade of D-.

**Equivalent(s):** MATH 605G

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- In the subject area of discrete mathematics, the candidate shall have the ability to: (a) Apply the fundamental ideas of discrete mathematics in the formulation and solution of problems arising from real-world situations (b) Use technology to solve problems involving the use of discrete structures
- In the subject area of discrete mathematics, the candidate shall demonstrate knowledge of: (a) Historical development of discrete mathematics (b) Basic elements of discrete mathematics, including but not limited to: (i) Graph theory (ii) Propositional logic (iii) Mathematical induction (iv) Recurrence relations (v) Finite differences (vi) Linear programming (vii) Combinatorics (Standard ~ 612.18 NH (9.a-b) ; Standard ~ 612.17 NH (9.a-b)

**MTH 709 - Linear Algebra **

**Credits:** 4

This course examines concepts in algebra including: patterns and functions, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greater common divisor, inequalities, modular arithmetic and systems of numbers, properties of groups and fields, the field of complex numbers, polynomial arithmetic and algebra, linear equations. The course develops the mathematical structures, algebraic properties, and applications of matrices, determinants, vectors, vector spaces, systems of linear equations, and linear transformations. Students engage with these concepts through exploration, analysis, proof, and problem solving based on activities used in secondary and middle school mathematics. Throughout the course students are given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.

**Prerequisite(s):** MTH 707 with a minimum grade of D- or MATH 607G with a minimum grade of D-.

**Equivalent(s):** MATH 604G

**Mutual Exclusion:** No credit for students who have taken MATH 545.

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Demonstrate a capacity to use physical materials and models to explore and explain the operations and properties of real and complex numbers with extensions to matrices and vectors.
- Identify and illustrate the mathematics underlying the theory of groups, rings, fields, and the relationships among them.
- Demonstrate a capacity to apply concepts of integer and rational exponents through modeling and applications. (Standard ~ 612.18 NH (4.h-j))
- Explain the distinctions among real numbers and their subsets with connection to field axioms.
- Demonstrate a capacity to apply the concepts of exponents, including integer and rational, through modeling and applications. (Standard ~ 612.17 NH (4.h-l))
- Model and analyze change and rates of change in various contexts.
- Use mathematical models to understand, represent, and communicate quantitative relationships, including, but not limited to equality, equations, inequalities, and proportional relationships.
- Explore, analyze, and generalize a wide variety of patterns and functions using multiple representations including tables, graphs, written word, and symbolic rules.
- Represent information to solve problems using matrices.
- Using graphing utilities and other technological tools to represent, explain, and explore algebraic ideas including functions, equations, and expressions
- Demonstrate knowledge of the historical development of algebra.
- Generalize patterns and functions using recursive and explicit representations.
- Articulate the meaning of functions and their inverse relationships, both formally and informally, with the use of concrete materials and graphing utilities
- Understand and compare the properties of classes of functions and their inverses, including exponential, polynomial, rational, step, absolute value, root, logarithmic, and periodic, including trigonometric.
- Understand and apply major concepts of: a. Linear algebra, including vector spaces and matrices; and b. Abstract algebra, including groups, rings, and fields
- Connect major concepts of linear and abstract algebra to the complex number system and other mathematical structures.
- Understand, identify, and apply arithmetic and geometric sequences, including partial sums of infinite arithmetic and geometric sequences, with connections to linear and exponential functions. (Standard ~ 612.18 NH (6.a-l) ; Standard ~ 612.17 NH (6.a-l)

**MTH 710 - Algebra Theory for Middle School Teachers **

**Credits:** 4

This course will examine concepts in algebra including patterns and functions, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greatest common divisor, inequalities, modular arithmetic and systems of numbers, basic properties of groups and fields, and polynomial arithmetic and algebra. This course will develop mathematical structures, algebraic properties, and applications of matrices. Students will engage with these concepts through exploration, analysis, proof, and problem solving based on activities used in middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.

**Prerequisite(s):** (MTH 402 with a minimum grade of D- or MATH 502G with a minimum grade of D-) and (MTH 705 with a minimum grade of D- or MATH 606G with a minimum grade of D-).

**Equivalent(s):** MATH 609G

**Grade Mode:** Letter Grading

### View Course Learning Outcomes

- Demonstrate a capacity to use physical materials and models to explore and explain the operations and properties of real and complex numbers with extensions to matrices and vectors. (a) Represent, use, and apply introductory concepts and properties of complex numbers. (b) Identify and illustrate the mathematics that underlies the procedures used for operations involving real numbers and their subsets. (c) explain the distinctions among real numbers and their subsets with connection to field axioms. (d) Demonstrate a capacity to apply the concepts of exponents, including integer and rational, through modeling and applications. (e) Connect the ideas of algebra and geometry through the use of coordinate geometry, graphing, vectors, and motion geometry. (f) Model and analyze change and rates of change in various contexts. (g) use mathematical models to understand, Represent, and communicate quantitative relationships, including, but not limited to equality, equations, inequalities, and proportional relationships. (h) explore, analyze, and generalize a wide variety of patterns and functions using multiple representations including tables, graphs, written word, and symbolic rules. (i) Represent information and solve problems using matrices. (j) use graphing utilities and other technological tools to Represent, explain, and explore algebraic ideas including functions, equations, and expressions (k) Demonstrate knowledge of the historical development of algebra (l) generalize patterns and functions using recursive and explicit representations (m) understand, Identify, and apply arithmetic and geometric sequences (n) Articulate the meaning of functions and their inverse relationships, both formally and informally, with the use of concrete materials and graphing utilities (o) understand and compare the properties of classes of functions and their inverses, including exponential, polynomial, rational, step, absolute value, root, logarithmic, and periodic, including trigonometric (p) Represent and analyze group and field properties of real numbers and other mathematical structures

**MTH 744 - Special Topics: Upper Level **

**Credits:** 1-4

A study of current and variable topics in mathematics. Course content will change from term to term.

**Repeat Rule:** May be repeated up to unlimited times.

**Equivalent(s):** MATH 644G

**Grade Mode:** Letter Grading