## Mathematics and Physics Department

The Department of Mathematics & Physics provides students with a strong foundation in using mathematics as a tool to solve complex, real-world problems. Whether a student wants to pursue graduate study, teach math, or apply mathematics in a quantitative STEM field, the study of mathematics adds up to an intellectual experience, which, from the abacus to the rocket, has been essential to civilization. A degree in mathematics from CSS develops a strong analytical ability, exposes students to the power of mathematics as a lens for viewing reality, and empowers students to continue their education after they graduate.

## Programs

The Mathematics Department offers these programs:

## Secondary Education

A B.A. in Mathematics with Middle/Secondary Education is also available.

## Contact Information

## Mathematics Courses

**MTH 1110 -**

**Mathematics in Society and Nature (Foundations : VFMA - Mathematics)**

**- 4 cr.**

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 information, growth models, a basic introduction to data, probability and statistics, game theory, voting theory, number systems, geometry and fractals, and mathematics in nature.

**Prerequisite Courses:**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 Courses:**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 Courses:**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 Courses:**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 Courses:**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 Courses:**Precalculus or ACT Math score of at least 29.

**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 Courses:**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.

**Prerequisite Courses:**MTH 1111, Java Programming language or instructor's permission.

**MTH 2442 -**

**Introduction to Data Analysis and Applied Statistics (Foundations : VFMA - Mathematics)**

**- 4 cr.**

Covers the fundamentals of data analysis and applied statistics with particular emphasis on the reasoning behind techniques and the entirety of a data focused investigative process. Students will have the opportunity to work with real data, use a statistical programming language, and perform entire analyses on data from asking initial questions to communicating final conclusions. Common statistical topics include inference with resampling methods, inference with probability distributions, and simple linear regression.

**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 Courses:**MTH 2401 or instructor's permission.

**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 Courses:**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 Courses:**MTH 2222 or instructor's permission.

**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.

**Prerequisite Courses:**MTH 2222.

**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.

**Prerequisite Courses:**completion of at least five mathematics courses in the major program including Cal. II and Discrete Math I. Co-requisite: EDU 3800.

**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.

**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 Courses:**MTH 3322 or instructor's permission.

**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 Courses:**MTH 2222.

**MTH 4421 -**

**Principles of Analysis I**

**- 4 cr.**

**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 Courses:**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 Courses:**permission of instructor.

**MTH 4999 -**

**Independent Study**

**- 1-4 cr.**

Research projects for upper-division students.

**Prerequisite Courses:**permission of instructor.

## Physics courses

**PSC 1201 -**

**Concepts of Physics (Conceptions : VCNS - Natural Science)**

**- 4 cr.**

A discovery course in which student groups design experiments, collect and analyze data which will help them to understand the processes of science and the basic concepts and laws of Newtonian mechanics, properties of matter, electricity and magnetism and energy, and waves. Conceptual understanding is stressed; some simple algebra is used. Mainly for elementary and middle school teacher education students.

**PSC 1501 -**

**A Short Course in Physics**

**- 4 cr.**

Selected topics from introductory physics for students who wish or need an understanding of physical concepts for their professional or personal enrichment. Some hands-on activities. Topics include force and motion, energy, waves, momentum, fluid mechanics, heat, sound, light, electricity and magnetism. Problem solving at the level of elementary algebra.

**PSC 1777 -**

**Physics (Conceptions : VCNS - Natural Science)**

**- 2,4 cr.**

Topics in Physical Science.

**PSC 2001 -**

**Physics I**

**- 0,4 cr.**

Covers algebra-based general physics including Newtonian mechanics (motion, force, energy, momentum), harmonic motion, fluids, and thermodynamics. Students must have ease and familiarity with basic algebraic and trigonometric techniques. Includes one 2-hour laboratory per week.

**Prerequisite Courses:**A grade of C (2.0 on a 4.0 scale) or better in College Algebra (MATH 1111) or a C or better in a more advanced college math course or a math ACT score of 24 or higher or by permission of the instructor.

**PSC 2002 -**

**Physics II**

**- 0,4 cr.**

Continues the study of algebra-based general physics including content in electricity and magnetism, geometric optics, sound and light waves, and selected topics in modern physics. Includes one 2-hour laboratory per week.

**Prerequisite Courses:**A grade of C (2.0 on a 4.0 scale) or better in PSC 2001.

**PSC 2011 -**

**General Physics I**

**- 4 cr.**

This course and its continuation PSC 2012 serve as a two-semester introduction to classical and modern physics using calculus. Topics include principles of classical mechanics: descriptions of motion, force, torque, and rotational motion, energy, momentum, and their conservation: fluid mechanics, simple harmonic motion, wave motion, and sound.

**PSC 2012 -**

**General Physics II**

**- 0,4 cr.**

Introduces the principles of electricity and magnetism, geometric optics, sound and light waves, and selected topics in modern physics. This is the second course in a two-course calculus-based general physics sequence. The physical principles and applications involved in these studies tend to be more abstract than the laws of mechanics that were studied in the first course in the sequence. In this course, many of the principles studied involve forces whose effects cannot be seen directly. Some of the forces studied only affect minute, invisible particles. Students will study models of unseen events and particles using graphs, sketches, analogies, mathematics, and descriptions. They will study the effects of the laws of physics using abstract models. Includes a 2-hour laboratory per week.