## MATHEMATICS

## DEPARTMENT

This introductory course in abstract algebra focuses mainly on number theory, with an introduction to groups and fields. Number-theoretic concepts include divisibility, primes and their distribution, congruence arithmetic, linear Diophantine equations and systems, number-theoretic functions, Euler's Theorem, primitive roots, and selected special topics.

This course continues the study of abstract algebra and is focused mainly on groups, with some exploration of rings and fields as time allows. Group-theoretic topics include subgroups, normal subgroups and quotient groups, and some counting principles. A wide variety of examples will be explored. Cross-listed: None. Offered: S, even years Prerequisite: MATH 441 with a grade of C or above.

This course focuses on the arithmetic and algebraic content of Pre-K-8 mathematics and appropriate teaching methods and is designed specifically to address requirements for MC-EA licensure. Instruction will be guided by the Common Core State Standards for Mathematics and the NCTM Principles and Standards for School Mathematics. Emphasis is on problem solving, critical thinking, and communication. This course does NOT satisfy the college general education requirement in math. Cross-listed: None. Offered: S Prerequisite: MATH 101 with a grade of "C" or above.

BASIC COLLEGE MATH
MATH 096
MATH
(3.00 credits)

This lab style, self-paced course supports students in developing skills, strategies, and reasoning needed to succeed in mathematics at Edgewood College. With the support of faculty, students will practice basic math skills in online modules and assess their knowledge throughout the semester. Credit does not count towards graduation requirements.

An introduction to differential and integral calculus. Derivatives are developed for: algebraic, logarithmic, exponential, trigonometric, and inverse trigonometric functions. The Riemann integral and the first form of the Fundamental Theorem of Calculus are introduced. Definite integrals and anti-derivatives are developed for basic algebraic, exponential, logarithmic, and trigonometric functions. Applications of key concepts are integrated throughout the course. This course satisfies the general education mathematics requirement. Cross-listed: None. Offered: F/S Prerequisite: Placement - or - MATH 114B with a grade of C or above - or - high school calculus.

CALCULUS II
MATH 241
MATH
(4.00 credits)

An introduction to multivariable calculus; topics include vectors, curves, partial derivatives, gradients, multiple and iterated integrals, and Green's and Stokes' theorems.

CALCULUS III
MATH 251
MATH
(4.00 credits)

This course is a continuation of differential and integral calculus. Topics include integration techniques, improper integrals, applications, differential equations, Taylor polynomials, and infinite series. This course emphasizes the mastery of key concepts and their applications.

This course investigates geometry from an advanced perspective. Building on students' knowledge of Euclidean geometry from high school coursework, topics include axiomatic systems, neutral, Euclidean, and non-Euclidean geometries; introduction of geometries such as projective, finite, vector, and transformational; historical development of geometry; and use of technology to model and explore geometric relationships.

This course continues the study of analysis shifting from the real numbers to complex numbers. Topics include functions of a complex variable, Cauchy's theorem, residue theory, power series, and other topics as time allows. Cross-listed: None. Offered: varies Prerequisite: MATH 233, MATH 301 with grades of C or above. MATH 431 recommended.

Theory of ordinary differential equations with an emphasis on problems of the physical world which are modeled well by differential equations. Topics include first order equations, second order and higher linear equations, series solutions, and a brief introduction to numerical methods and partial differential equations as time permits. Cross-listed: None. Offered: S, odd years Prerequisite: MATH 232 with a grade of C or above; MATH 233 highly recommended.

DISCRETE MATHEMATICS
MATH 256
MATH
(3.00 credits)

This course introduces students interested in math or computer science to a level of abstraction and argumentation appropriate to those fields as well as providing some of the foundational mathematics – and more importantly, ways of thinking – needed for success in either field. In addition, the course provides students the opportunity to see connections between the two fields such as those between symbolic logic and digital logic circuits or between recurrence and induction. Topics include: logic, methods of proof, sequences, induction, recursion, set theory, functions, relations, counting, probability, graphs, trees, analysis of algorithm efficiency.

This course focuses on mathematics knowledge for teaching at the middle/secondary level and is designed specifically to address requirements for MC-EA licensure with content minor in mathematics and EA-A licensure with content major in mathematics. Instruction will be guided by the Common Core State Standards for Mathematics and the NCTM Principles and Standards for School Mathematics. Topics include: problem solving, critical thinking, communication, issues of technology, number and operations, algebraic and geometric reasoning, measurement, and data analysis and probability.

An introduction to finite mathematics, including linear systems, linear programming, mathematics of finance, probability, and other related topics. This course is designed primarily for business majors. This course does NOT satisfy the general education mathematics requirement. Cross-listed: None. Offered: F/S Prerequisite: Placement or MATH 114A with a grade of C or above.

This course focuses on the geometric and measurement content of Pre-K-8 mathematics and appropriate teaching methods and is designed specifically to address requirements for MC-EA licensure. Instruction will be guided by the Common Core State Standards for Mathematics and the NCTM Principles and Standards for School Mathematics. Emphasis is on problem solving, critical thinking, and communication. This course does NOT satisfy the college General Education mathematics requirement. Cross-listed: None. Offered: F Prerequisite: MATH 102 with a grade of "C" or above.

INDEPENDENT STUDY - MATHEMATICS
MATH 279
MATH
(1.00 - 4.00 credits)

Independent study of selected topics in mathematics developed by the student with the approval and direction of the instructor. Cross-listed: None. Offered: No Information Provided. Prerequisite: consent of instructor.

INDEPENDENT STUDY - MATHEMATICS
MATH 079
MATH
(1.00 - 4.00 credits)

Cross-listed: None. Offered: No Information Provided. Prerequisite: consent of instructor.

INDEPENDENT STUDY - MATHEMATICS
MATH 479
MATH
(1.00 - 4.00 credits)

Independent reading and research of selected topics in mathematics developed by the student with the approval and direction of the instructor. Cross-listed: None. Offered: No Information Provided. Prerequisite: consent of instructor.

INDEPENDENT STUDY - MATHEMATICS
MATH 379
MATH
(1.00 - 4.00 credits)

Independent study of selected topics in mathematics developed by the student with the approval and direction of the instructor. Cross-listed: None. Offered: No Information Provided. Prerequisite: consent of instructor.

INTERMEDIATE ALGEBRA
MATH 097
MATH
(3.00 credits)

This course is designed to provide students with a strong foundation in algebra, graphing, and problem-solving skills. Successful completion of this course should give students the necessary prerequisite skills to be successful in MATH 114A M - Precalculus A: College Algebra. (ALEKS or ACT Placement) Cross-listed: None. Offered: No Information Provided. Prerequisite: Placement Level One.

An introduction to problem solving and mathematical thinking; the focus of this course is on the process of mathematics rather than specific techniques or content. Students will engage in mathematical problem solving in a variety of contexts and learn a number of broadly applicable problem solving strategies. This course satisfies the M tag General Education requirement. Cross-listed: None. Offered: F/S Prerequisite: placement - or - grade of P in MATH 096 - or - grade of PR in Math 96 and concurrent enrollment in ENG 099A.

An introduction to linear algebra including vector spaces, matrices, linear transformations, eigenvalues and eigenvectors; emphasis on gaining theoretical insights through computation, developing facility with elementary proof, and applying the concepts and computational methods to solve real world problems.

Selected topics in mathematics, mathematics education, and applications. With individualized mentoring, students will investigate significant mathematics independently and present findings in oral and written form at a variety of levels and to varying audiences. Integrated throughout the course students will 1) consider how topics are situated in the history and development of mathematics as a liberal art, and in the world; 2) reflect, as future mathematics educators and practitioners, upon: Who am I and who can I become? What are the needs and opportunities of the world? What is my role in building a more just and compassionate world? Cross-listed: None. Offered: F Prerequisite: COR 2, junior/senior standing, and a declared major in Mathematics or Mathematics Teaching; or consent of the instructor.

Algebra preparation necessary for success in calculus. Topics include: algebraic properties of linear, quadratic, polynomial, rational, exponential and logarithmic functions and their graphs. Combined with Math 114B: Precalculus B: Trigonometry, the two courses comprise a complete overview of algebra and trigonometry required for calculus. This course satisfies the general education mathematics requirement.

Trigonometry preparation necessary for success in calculus. Topics include: trigonometric functions and their inverses, including identities, graphs, and applications. Combined with MATH 114A the two courses comprise a complete overview of algebra and trigonometry required for calculus.

A calculus-based introduction to probability. Topics include combinatorics, discrete and continuous probability distributions and joint probability, binomial, Poisson, exponential, and normal distributions, expected value, variance, and moment generating functions. This course will provide a solid introduction to probability and prepare interested students for the first actuarial exam. Cross-listed: None. Offered: S, even years Prerequisite: MATH 232 with a grade of C or above.

This course is intended as a gateway to upper-level mathematics courses. The emphasis is on creative problem solving strategies, structures, and techniques of proof, as well as effective oral and written communication of mathematical ideas. It is designed to ease the transition from algebra and calculus to more theoretical courses such as abstract algebra, geometry and real analysis. Cross-listed: None. Offered: F Prerequisite: MATH 231 with a grade of C or above, and sophomore status.

The course introduces analysis as a tool for a deeper understanding of calculus. With the least upper bound axiom of the real numbers as its starting point, the course develops the foundations necessary to work with limits and prove results from calculus. Topics include sequences, series, power series, derivatives, and integrals. Time permitting, the course will explore how the same tools are used in more advanced settings.

This course explores arithmetic, algebra, and data analysis at the Middle Childhood/Early Adolescence level as defined in the Common Core State Standards for Mathematics; best practices and methodologies for teaching this content; and relevant research in teaching and learning mathematics. A fifteen-hour practicum is required. Cross-listed: None. Offered: SS Prerequisite: MATH 101 with a grade of C or above and successful completion of Praxis CORE. For students in the ACE program only.

This course explores geometry, measurement, and probability at the Middle Childhood/Early Adolescence level as defined in the Common Core State Standards for Mathematics; best practices and methodologies for teaching this content; and relevant research in teaching and learning mathematics. A fifteen-hour practicum is required. Cross-listed: None. Offered: F Prerequisite: MATH 602 with a grade of C or better. For students in the ACE program only.

Course includes descriptive and inferential statistics with the emphasis on drawing meaningful conclusions from data. Topics include measures of central tendency and dispersion, the normal distribution, z-tests, t-tests, linear regression, analysis of variance, Chi-Square tests, and other topics as time permits. This course satisfies the general education mathematics requirement.

SUCCESS IN MATH STATISTICS
MATH 099B
MATH
(2.00 credits)

This course is intended for students who may need additional instruction on the material covered in Statistics. Topics covered will include strengthening quantitative literacy and improving math study skills. Cross-listed: None. Offered: F/S Prerequisite: ACT Math score of 16 or above; or ALEKS test score of 31 or above.

SUCCESS IN PRE-CALCULUS
MATH 099C
MATH
(2.00 credits)

This course is intended for students who may need additional instruction on the material covered in Pre-Calculus. Topics covered will include strengthening quantitative literacy and improving math study skills. Must be taken concurrently with MATH 114A.

SUCCESS IN PROBLEM SOLVING
MATH 099A
MATH
(2.00 credits)

This course is intended for students who may need additional instruction on the material covered in Introduction to Problem Solving. Topics covered will include strengthening quantitative literacy and improving math study skills. Must be taken concurrently with MATH 101. Cross-listed: None. Offered: No Information Provided. Prerequisite: ACT Math score of 16 or above; or ALEKS test score of 31 or above.

This course is designed to provide an integrative study of curriculum and instruction in mathematics for middle/secondary level teaching including appropriate research and practice in learning theories, curriculum development, teaching methods, instructional materials, evaluation and assessment. Instruction will be guided by the Common Core State Standards for Mathematics and the NCTM Principles and Standards for School Mathematics. Cross-listed: ED 459M and ED 651. Offered: F Prerequisite: Praxis CORE, Praxis Subject test in Mathematics, and completion of the Emergent Professional Transition.

This course focuses on properties of spaces invariant under homeomorphisms. Topics include continuity, homeomorphisms, connectedness, compactness, manifolds, the classification of closed, compact surfaces, the Euler characteristic, the fundamental group, and knot theory.