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# Courses

**MATH 017: MATH PATHWAYS*** 3 credit hrs. *Math Pathways focuses on developing an understanding of how data and mathematical tools can be employed to inform citizens about real-world situations. The course focuses on three broad themes: (1) quantitative thinking and reasoning, (2) understanding data analysis, and (3) mathematical modeling with technology tools. Students will learn the foundational ideas in each of these areas and explore real-world applications. Math Pathways is a mathematics course for liberal arts students who would like to fulfill the quantitative AOI requirement and for business students who are preparing to take business calculus. Students wishing to take additional mathematics before precalculus can also enroll in this course.

Prereq.: None.

**MATH 020: PRECALCULUS: ALGEBRA & TRIGONOMETRY**

Prereq.: Completion of high school mathematics through Algebra II.

**MATH 024: ****STRUCTURE OF MATHEMATICS FOR ELEMENTARY EDUCATION I**, 3 credit hrs.

Basic concepts and structure of whole numbers, integers, rational numbers, decimals, and real numbers and operations on these number sets as they relate to the K-6 curriculum. Also proportional reasoning, algebraic reasoning, and statistics appropriate to the elementary school curriculum are discussed. Restricted to elementary education majors, or middle school endorsement.

Prereq.: Completion of high school mathematics through Algebra II/Geometry.

**MATH 025: ****STRUCTURE OF MATHEMATICS FOR ELEMENTARY EDUCATION II**, 3 credit hrs.

Continuation of Math 024, with emphasis on the content strands of problem solving, number theory, probability, geometry, and measurement. Restricted to elementary education majors, or middle school endorsement.

Prereq.: Completion of high school mathematics through Algebra II/Geometry.

**MATH 028: ****BUSINESS CALCULUS**, 3 credit hrs.

Brief algebra review, data analysis, limits, derivatives, integration, applications to business.

Prereq.: MATH 017 or completion of high school mathematics through Algebra II or equivalent.

**MATH 050: ****CALCULUS I**, 3 credit hrs.

Very brief review of algebra, logarithms, and trigonometry; functions; introduction to continuity, limits, differentiation, and integrals, with applications.

Prereq.: MATH 020 or equivalent pre-calculus course.

**MATH 054: ****INTRODUCTION TO DISCRETE MATHEMATICS**, 3 credit hrs.

Number systems, algorithms, sets, logic, Boolean algebra, functions, combinatorics, probability, graph theory.

Prereq.: MATH 020 or equivalent.

** MATH 061: GEOMETRY FOR 6-12 TEACHERS**,

**MATH 062: ***STATISTICS AND PROBABILITY FOR 6-12 MATHEMATICS TEACHERS*,

The subject matter of the course, statistics and probability, will be grounded in experiences that arise in the context of teaching in order to simultaneously build content and pedagogical knowledge with a focus on the use of real-world data and technology tools. The choice of activities will span the content required by the Common Core Standards of Mathematics for middle and high school with connections to more advanced content.

Prereq.: Sophomore status and enrollment in either an education program or mathematics education major.

**MATH 063: ALGEBRA AND MODELING FOR 6-12 TEACHERS**,

Prereq.: Restricted to Education Majors.

**MATH 064: TUTORING IN MATHEMATICS & COMPUTER SCIENCE**

1 credit hr.

Prereq.: Math 050 or equivalent.

**MATH 070: ****CALCULUS II**, 3 credit hrs.

Advanced applications of differentiation; advanced techniques and applications of integration; simple examples of differential equations.

Prereq.: MATH 050.

**MATH 080: ****LINEAR ALGEBRA**, 3 credit hrs.

Systems of linear equations; vectors, linear independence, linear transformations; matrix operations, inverse of a matrix, determinants; null and column space of a matrix, rank; general vector spaces, basis of a vector space, dimension; eigenvalues and eigenvectors, diagonalization, orthogonality; applications.

Prereq.: MATH 050.

**MATH 099: ****INDEPENDENT STUDY**, 1-3 credit hrs.

Directed individual study in areas related to the student's needs or interest.

Prereq.: Consent of department.

**MATH 100: CALCULUS III**

Infinite series and sequences, power series, and Taylor series. Plane curves; introduction to limits, continuity, differentiation, and integration for functions of several variables.

Prereq.: MATH 070.

**MATH 101:**** MATHEMATICAL REASONING**, 3 credit hrs.

Logic; sets and mappings; methods of proof including direct and indirect proofs, induction, Delta-Epsilon arguments; axiomatic systems.

Prereq.: MATH 070, 080. Coreq.: MATH 100. *Note-Math 101 is a prereq. for:*** **MATH 150, 153, 155, 157, 176, 184 and 187.

**MATH 110: ****MULTIVARIATE CALCULUS**, 3 credit hrs.

Properties of continuous mappings from Rn to Rm, differential forms, vector calculus. Line integrals. Stokes' theorem.

Prereq.: MATH 080, 100.

**MATH 120: ****APPLIED DIFFERENTIAL EQUATIONS I**, 3 credit hrs.

Ordinary differential equations; systems of differential equations. Fourier series, integrals and harmonic analysis, partial differential equations, orthogonal functions. Bessel functions. Legendre functions.

Prereq.: MATH 070, 080. Coreq.: MATH 100.

**MATH 121: ****APPLIED DIFFERENTIAL EQUATIONS II**, 3 credit hrs.

Continuance of MATH 120.

Prereq.: MATH 120. Coreq.: MATH 110.

**MATH 125: MATHEMATICAL MODELING**

The construction, analysis and interpretation of mathematical models. Examples are drawn from a variety of areas. Student projects are required.

Prereq.: CS 065, MATH 070, 080.

**MATH 126: INDUSTRIAL MATH**

This course is a project-oriented seminar that follows a course in Math 125: Mathematical Modeling. Concepts from calculus, linear algebra, differential equations and other areas of mathematics will be used to derive, describe and solve mathematical models from the life, physical, and social sciences. Familiarity with a programming language is desirable, but not required. The goal of this course is to provide students with multiple examples of how mathematics can be used to explain various phenomena, to describe real-world situations and to make (more quantitatively) informed decisions in industrial settings.

Prereq.: MATH 125.

**MATH 127: ****INTRODUCTION TO GAME THEORY**, 3 credit hrs.

Game Theory is the logical analysis of situations of conflict and cooperation. Topics will include zero-sum games and non-zero-sum two-person games, in person games, applications to economics, politics and nature.

Prereq.: MATH 070, 080

**MATH 130: PROBABILITY FOR ANALYTICS**

Prereq.: MATH 070, STAT 040.

**MATH 131: INTRODUCTION TO PROBABILITY I **(cross-listed with ACTS 131), 3

Prereq.: MATH 080, 100.

**MATH 139: THEORY OF COMPUTATION **(cross-listed with CS 139), 3

Prereq.: CS 65 and (MATH 054 or MATH 101).

**MATH 140: ****COOPERATIVE EDUCATION**, 1-3 credit hrs.

Students who are in a work environment related to the major field of study may receive credit for applications of classroom knowledge to their job. The student meets regularly with the adviser to determine appropriate assignments. May be repeated up to a maximum of eight hours of credit. (Graded on a credit/no credit basis).

Prereq.: At least junior standing or consent of instructor.

**MATH 144: ****TOPICS IN MATH EDUCATION**, 3 credit hrs.

Topics for elementary and secondary mathematics pre-service teachers include introduction to new and established curricular materials and development of classroom materials in the context of the National Council of Teachers of Mathematics "Principles and Standards for School Mathematics."

Prereq.: None.

**MATH 145: METHODS OF TEACHING SECONDARY SCHOOL MATHEMATICS**

Instructional strategies and materials for teaching secondary school mathematics. Restricted to secondary education majors.

Prereq.: Consent of instructor.

**MATH 148: COUNTING WITH COMBINATORICS**

An introduction to enumerative combinatorics. This course examines techniques for enumerating and counting a variety of combinatorial objects including subsets, multisets, lists, permutations, compositions, and partitions. More advanced topics include the twelve-fold way, the principle of inclusion-exclusion, and generating functions.

Prereq.: MATH 101.

**MATH 150: Graph Theory **(cross-listed with CS 150)

An introduction to the structural theory of graphs and networks with applications to computer science. Topics may include basic graph families and parameters, algorithms, matchings, connectivity, flows and networks, traversability, planarity, and colorings.

Prereq.: CS 065 and MATH 101.

**MATH 153: ****MODERN GEOMETRY**, 3 credit hrs.

A rigorous approach to Euclidean and non-Euclidean geometries from a general, axiomatic point of view.

Prereq.: MATH 101.

**MATH 155: INTRODUCTION TO ABSTRACT ALGEBRA I**

An introduction to group theory, including symmetric groups, dihedral groups, cyclic groups, homomorphisms and isomorphisms, normal subgroups, quotient groups, Noether’s isomorphism theorems.

Prereq.: MATH 101.

**MATH 156: *** INTRODUCTION TO ABSTRACT ALGEBRA II, 3 credit hrs. *An introduction to rings, fields, and advanced group theory. Topics may include Groebner bases, field extensions, Galois theory, cryptography, coding theory, and Boolean algebras.

Prereq.: MATH 155.

**MATH 157: HISTORY OF MATHEMATICS**

An overview of the evolution of mathematics from ancient times through Newton and Leibniz. The conceptual development of mathematics will be emphasized.

Prereq.: MATH 101.

**MATH 165: INTRODUCTION TO NUMERICAL ANALYSIS**

(cross-listed with CS 165)

Error analysis, iterative methods for solving nonlinear equations, direct and iterative methods for solving linear systems, approximation of functions, derivatives, integrals.

Prereq.: CS 065, MATH 080 and 100.

**MATH 176:**** ADVANCED LINEAR ALGEBRA**, 3 hrs.

Hermitian, unitary, normal, positive definite and nonnegative matrices; LU, QR and Choleski factorizations; equivalence, similarity, congruence and their respective canonical forms; norms; Schur triangular form, Jordan canonical form; applications.

Prereq.: MATH 101.

**MATH 184: INTRODUCTION TO REAL ANALYSIS I**

Algebraic and topological properties of the real line. Limits, continuity, differentiation. Riemann integration, series.

Prereq.: MATH 101, 110.

**MATH 185: ****INTRODUCTION TO REAL ANALYSIS II**, 3 credit hrs.

Continuance of MATH 184.

Prereq.: MATH 101, 110.

**MATH 187: ****COMPLEX ANALYSIS**, 3 credit hrs.

Algebraic and topological properties of the complex plane. Theory of analytic functions. Applications.

Prereq.: MATH 100, 101.

**MATH 191: ****MATHEMATICS CAPSTONE**, 1 credit hr.

The purpose of a capstone is for students to undertake an independent project that applies and synthesizes what they have learned in their major. This course is typically taken in one of the student's final two semesters at Drake. One outcome will be a written project that can take several forms, for example a research paper or a software package. A second outcome is a presentation of their work to the students and faculty of the department, usually during the last two weeks of the semester.

**MATH 192: ****MATH SECONDARY EDUCATION CAPSTONE**, 1 credit hr.

The purpose of a capstone is for students to undertake an independent project that applies and synthesizes what they have learned in their major. This course should be taken prior to student teaching and may be taken in the second semester of the junior year. One outcome will be a written project that can take several forms, for example a research paper, an educational software package, or lesson plans. A second outcome is a presentation of their work to the students and faculty of the department, usually during the last two weeks of the semester.

**MATH 195: TOPICS IN THE MATHEMATICAL SCIENCES**

Seminars in selected topics.

Prereq.: Consent of instructor.

**MATH 199: ****INDEPENDENT STUDY**, 1-3 credit hrs.

Directed individual study in areas related to the student's needs or interest.

Prereq.: Consent of department.

**MATH 230: ****INDEPENDENT STUDY**, 1-3 credit hrs.

**MATH 245: ****TOPICS FOR SCHOOL MATHEMATICS**, 3 credit hrs.

Seminars in selected topics.

Prereq.: Consent of instructor.