# Mathematics Course Descriptions

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MTH 1110 - Liberal Arts Mathematics ( Foundations: VFMA - Mathematics ) - 4 cr.
This course covers mathematical topics of use and/or interest to students who do not need a technical course in algebra to succeed in sciences or pre-calculus. Topics cover a broad range such as the interpretation of graphical data, basic properties of exponential functions, an introduction to the basics of probability and statistics, game theory, voting theory, the real number system, geometry and fractals, and mathematics in nature. Prerequisite: three years of high school math or instructor's permission.

MTH 1111 - College Algebra ( Foundations: VFMA - Mathematics ) - 4 cr.
Topics include a brief review of elementary algebra, introduction to polynomial, exponential, logarithmic and trigonometric functions using both symbolic and graphic approaches. Emphasis is on applications in a variety of disciplines and solutions of real-world problems. Students planning to continue mathematics receive appropriate preparation. Prerequisite: three years of high school math or instructor's permission.

MTH 1113 - Mathematical Ideas I ( Foundations: VFMA - Mathematics ) - 4 cr.
Topics selected to give a broad view of mathematics needed for a liberal education. Investigations emphasize mathematics needed by prospective teachers of elementary grades to address the strands: patterns and functions; number sense from whole numbers to real numbers. Prerequisite: three years of high school mathematics or instructor's permission.

MTH 1114 - Mathematical Ideas II ( Foundations: VFMA - Mathematics ) - 4 cr.
Continuation of MTH 1113 for students intending to teach math in elementary grades and for liberal arts education. Topics include basic statistics and probability, measurement, space and shape in geometry. Prerequisite: three years of high school math or instructor's permission.

MTH 1122 - Precalculus ( Foundations: VFMA - Mathematics ) - 4 cr.
Precalculus mathematics, further properties of polynomial and rational functions, exponential and logarithmic functions, trigonometric functions and their graphs, trigonometric identities and equations, inverse trigonometric functions, introduction to analytic geometry. Formal mathematical language designed to help students succeed in college calculus courses. Prerequisite: MTH 1111 or Math ACT above 22.

MTH 1210 - Mathematical Ideas A ( Foundations: VFMA - Mathematics ) - 2 cr.
Addresses the full spectrum of K-8 math when combined with MTH1211, from a conceptual as well a procedural standpoint to meet the mathematical strands of the Minnesota Board of Teaching Standards for elementary teachers. Examines the concepts and diverse modalities by which students learn patterns and functions, problem solving, probability, sets, number sense, computational procedures, relationships of integers, properties of real numbers, and number theory including divisibility, factors, multiples, and prime factors. Learners analyze these concepts while examining the reasonableness of student's answers, drawing connections to real world applications, and as well showing understanding of the connections between various mathematical domains. Understanding of multiple problem solving methods for the concepts covered and understanding the mathematical properties and processes involved are key focuses of the course. Admission to this course requires Graduate Teaching Licensure Program enrollment, or permission of the instructor, based on having ACT math sub-score 26 or higher.

MTH 1211 - Mathematical Ideas B ( Foundations: VFMA - Mathematics ) - 2 cr.
Addresses the full spectrum of K-8 math when combined with MTH1210, from a conceptual as well a procedural standpoint, to meet the mathematical strands of the Minnesota Board of Teaching Standards for elementary teachers. Examines the concepts and diverse modalities by which students learn properties and relationships of 2D and 3D geometric figures, measurement, usage of geometric learning tools, data investigations, randomness and uncertainty, and algebraic representation. Learners will demonstrate knowledge and application of concepts from abstract and concrete perspectives as well as real world applications, quantitative and qualitative approaches to answering questions, ability to communicate mathematics effectively at a variety of levels, relationships between mathematics and other fields, how to integrate the history of math and the relations between various cultures and mathematics as well as how to integrate technological and tools with mathematics. Understanding of multiple problem solving methods for the concepts covered and understanding the mathematical properties and processes involved are key focuses of the course. Admission to this course requires Graduate Teaching Licensure Program enrollment, or permission of the instructor based on having ACT math sub-score 26 or higher.

MTH 2221 - Calculus I ( Foundations: VFMA - Mathematics ) - 4 cr.
Limits, continuity and fundamental theory of differentiation, symbolic and numerical calculations of derivatives, applications of derivatives; definite integrals and Riemann sums. Prerequisite: Precalculus or ACT Math score of at least 29.

Prerequisite Course: MTH 1122

MTH 2222 - Calculus II ( Foundations: VFMA - Mathematics ) - 4 cr.
Study of numerical integration, applications of definite integrals, improper integrals, sequences and infinite series, basic ideas and methods for solving differential equations. Prerequisite: MTH 2221.

Prerequisite Course: MTH 2221

MTH 2401 - Discrete Mathematics I ( Foundations: VFMA - Mathematics ) - 4 cr.
Elementary graph theory including matrix representation; coding and sorting applications; combinations and permutations; voting and apportionment; introduction to logic; elementary algorithm analysis and design; mathematical induction. Prerequisites: MTH 1111, Java Programming language or instructor's permission.

MTH 2777 - Topics in Math - 2-4 cr.
Topics.

MTH 3302 - Contemporary Geometry - 4 cr.
Foundations of Euclidean geometry, solid geometry; introductions to non-Euclidean geometry; spherical geometry. Course includes dynamic geometry investigations using appropriate software. Prerequisite: MTH 2401 or instructor's permission.

Prerequisite Course: MTH 2401

MTH 3321 - Multivariable Calculus - 4 cr.
Topics include functions of several variables, gradients, partial derivatives and multiple integrals, vector fields, Green's and Stoke's theorems, and applications. Prerequisite: MTH 2222.

Prerequisite Course: MTH 2222

MTH 3322 - Linear Algebra - 4 cr.
Further study of systems of linear equations, matrices and determinants, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, diagonalization. Prerequisite: MTH 2222 or instructor's permission.

Prerequisite Course: MTH 2222

MTH 3323 - Differential Equations - 4 cr.
Introduction to the theory of differential equations, varied methods to solve linear, nonlinear equations, quantitative analysis of solutions of equations. Prerequisites: MTH 2222.

Prerequisite Courses: MTH 2222, MTH 3321

MTH 3533 - Mathematics Teaching Methods - 4 cr.
This course consists of two portions. Secondary planning for mathematics instruction includes classroom observations and the study of mathematics curriculum, assessment, teaching methods and resources for teaching and learning aids. Highlights of math related to high school teaching revisit some important concepts in core math courses. Prerequisites: completion of at least five mathematics courses in the major program including Cal. II and Discrete Math I. Co-requisite: EDU 3800.

Prerequisite Courses: MTH 2222, MTH 2401

MTH 3535 - Math Methods Field Experience - 1 cr.
Introduces students to the culture of a high school environment. They observe and assist a math teacher, interview school personnel, talk with students, and teach technology-integrated math lessons and content area reading strategies. Assessment practices are observed and practiced. Co-requisite: MTH 3533.

Prerequisite Courses: EDU 2800, EDU 2805

MTH 4332 - Abstract Algebra I - 4 cr.
Introduction to groups, ring and field theory; group homomorphism and isomorphism, Cayley's theorem, and quotient groups, Lagrange's theorem; rings, ideals, ring homomorphism and basic properties of fields. Prerequisite: MTH 3322 or instructor's permission.

Prerequisite Course: MTH 3322

MTH 4411 - Probability and Statistics I - 4 cr.
A survey course in mathematical probability and statistics. It includes probability distributions and densities, mathematical expectations, functions of random variables, introduction to estimation theory and hypothesis testing and applications. Prerequisite: MTH 2222.

Prerequisite Course: MTH 2222

MTH 4412 - Probability and Statistics II - 2 cr.
Study of multivariate distributions, theory of estimation, hypotheses testing, and statistical inference and their applications. Prerequisites: MTH 4411 and MTH 3321.

Prerequisite Courses: MTH 3321, MTH 4411

MTH 4421 - Principles of Analysis I - 4 cr.
Introduction to real analysis. It includes completeness of the real number system, topology of the real line, sequences, convergence, limits, continuity, differentiability and the Riemann integral, the Fundamental Theorem of Calculus. Prerequisites: MTH 3321,MTH 3322.

Prerequisite Courses: MTH 3321, MTH 3322

MTH 4422 - Principles of Analysis II - 2 cr.
Sequences of functions, uniform convergence, the Bounded Convergence Theorem, infinite series, topology of the set of real numbers, Heine-Borel Theorem and metric spaces. Prerequisite: MTH 4421.

Prerequisite Course: MTH 4421

MTH 4432 - Abstract Algebra II - 2 cr.
More topics of rings and fields, maximal and principal ideals, complete ordered fields, polynomial rings, factorization in F[x], field extensions. Prerequisite: MTH 4332.

Prerequisite Course: MTH 4332

MTH 4500 - Senior Seminar - 2 cr.
This course is required for all Mathematics majors. Under the direction of Mathematics faculty, students pick topics in any area of math, do research/independent reading and write papers for presentation. Prerequisite: instructor's permission.

MTH 4555 - Math Internship - 1-8 cr.
Internship in Mathematics.

MTH 4777 - Topics in Math - 2-4 cr.
Concentrated study of various subject areas. Prerequisite: permission of instructor.

MTH 4999 - Independent Study - 1-4 cr.
Research projects for upper-division students. Prerequisite: permission of instructor.