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# Courses

## Mathematics

##

**MATH 017: ****SPIRIT OF MATHEMATICS**, 3 credit hrs.

The nature of the topics will vary but will expose students to a wide variety of mathematics. Topics from advanced mathematics will be included but will be presented at a level appropriate to college students who do not have an extensive mathematical background. Topics will be chosen from a wide array of applications, such as financial mathematics, fractals, chaos, environmental mathematics, conceptions of space, the nature of infinity, encryption techniques and topics from the history of mathematics. Among the mathematical techniques that may be used: functions and equations (exponential, linear and quadratic); difference equations; equation solving techniques (algebraic and technological); problem solving and mathematical reasoning techniques; basic probability and statistics; graphical analysis; geometrical analysis; the concept of infinity. This course is not intended for STEM or business majors, or for students with previous credit in a college math course. Students who have taken previous college math must get the approval of the instructor. This course does not satisfy the prerequisites of any math courses. Prereq.: None.

**MATH 020: PRECALCULUS: ALGEBRA & TRIGONOMETRY***, 4 credit hrs.*

Study of linear, exponential, power, logarithmic, and polynomial functions from an algebraic, graphical and numerical point of view; fitting functions to data; review of trigonometry; solutions to equations and systems of equations. Prereq.: Completion of high school mathematics through Algebra II/Trigonometry.

**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 24, 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 020 or equivalent.

**MATH 050: ****CALCULUS I**, 4 credit hrs.

Analytic geometry concepts; functions; continuity; limits; differentiation; applications of derivatives; definite integrals; techniques of integration. Prereq.: MATH 020 or equivalent and exposure to trigonometry.

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

**MATH 063: Algebra and Modelling for 6-12 Teachers, 3 credit hrs.**The subject matter of the course, algebra and mathematical modeling, 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 situations 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. Students will develop essential understandings, learn how to use manipulatives and technology, explore and analyze curricular resources, build an awareness of learning progressions, discuss common student challenges and effective ways to address them, and create tasks and lessons that are engaging to students through use of real-world applications and explorations. Restricted to education majors.

**MATH 070: ****CALCULUS II**, 4 credit hrs.

Definite integrals; techniques of integration; applications of definite integrals, infinite series and sequences; power series; Taylor series. Prereq: Math 50.

**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**

Plane curves; vectors; limits, continuity and differentiation for functions of several variables; multiple integrals. Prereq.: Math 70

**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. Note: This course 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 080, 100.

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

Continuance of MATH 120. Prereq.: MATH 120.

**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.: MATH 070, 080.

**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, n person games, applications to economics, politics and nature. Prereq.: MATH 028 or MATH 050 or consent of instructor.

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

An introduction to probability concepts, including definition of probability: independence; conditional probability; independence; random variables; specific discrete and continuous probability distributions; multivariate random variables; moments and moment generating functions; functions of random variables; sampling distributions; and central limit theorem. Prereq.: MATH 080, 100.

**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 150: DISCRETE STRUCTURES** (cross-listed with CS 150)

The course covers subjects in discrete mathematics with applications to computer science. Topics include algorithms, graph theory and combinatorics. 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**

Introduction to groups, rings, integral domains and fields; homomorphisms and isomorphisms; properties of the integers; polynomial rings and factorization; field extensions. Prereq.: MATH 101.

**MATH 156: ****INTRODUCTION TO ABSTRACT ALGEBRA II**, 3 credit hrs.

Continuance of MATH 155. 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 100, 101.

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

Continuance of MATH 184. Prereq.: MATH 184.

**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.

January 23, 2020