## 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 1101 -**

**Mathematics for Elementary Education Majors I (Foundations : VFMA - Mathematics)**

**- 3 cr.**

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. Understanding of multiple problem-solving methods for the concepts covered and understanding the mathematical properties and processes involved is the primary focus of the course.

**MTH 1102 -**

**Mathematics for Elementary Education Majors II (Foundations : VFMA - Mathematics)**

**- 3 cr.**

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. Understanding of multiple problem-solving methods for the concepts covered and understanding the mathematical properties and processes involved are key focuses of the course.

**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 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 24.

**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:**MTH 1122, 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

**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

**MTH 3323 -**

**Differential Equations**

**- 4 cr.**

**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.

**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

**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 4501 -**

**Senior Seminar I**

**- 1 cr.**

The introduction to a math major’s Senior Project. Students will work with their faculty mentor to generate project ideas, develop a project plan, and do background research on their topic.

**MTH 4502 -**

**Senior Seminar II**

**- 1 cr.**

The culmination of a math major’s Senior Project. Students will finish their project paper and give a 30-minute presentation on their project at the end of the term.

**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 1202 -**

**Cosmic Systems**

**- 4 cr.**

A study of the universe as a set of interacting, evolving systems: galaxies, stars, the solar system and the Earth with its rocks, oceans and atmosphere. Study includes investigations of the matter-energy cycles in these systems and the effects of natural and human interventions upon them. In-class investigations and discovery activities and field trips are part of this course. Mainly for elementary and middle school teacher education students.

**PSC 1209 -**

**Overview of Astronomy**

**- 1 cr.**

Covers a broad introduction to astronomy including a study of the Earth-Moon system, the solar system, stars, and galaxies. The course is focused on topics required in the State of Minnesota space science standards for K-6 teachers.

**PSC 1210 -**

**Introduction to Physical Scien**

**- 2 cr.**

This course provides the basic content and concepts required for elementary and middle school teachers as outlined in the Minnesota Teacher Licensure standards. It will cover the major principles of Physical Science, including motion, waves, light, electricity, magnetism, properties of matter, chemical reactions, thermodynamics, and chemical kinetics. Tutorials and interactive activities, and discussion of concepts demonstrating basic principles of physical science will be presented to the student for analysis, thus allowing students to construct their own meaning of higher level concepts as presented in the text.

**PSC 1301 -**

**Explorations in Astronomy (Conceptions : VCNS - Natural Science)**

**- 4 cr.**

Explores a range of topics in astronomy including objects in our solar system, stars & stellar life cycles, galaxies, and cosmology. The course will present recent discoveries and observations, as well as discuss current issues in modern astronomy including cultural conflicts over how and where astronomy is practiced.

**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 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 (MTH 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.

**PSC 2777 -**

**Topics in Physical Science**

**- 0-4 cr.**

Occasional or special-purpose courses in physics, electronics, history or cultural aspects of science, on a level appropriate to the freshman or sophomore student.

**PSC 3777 -**

**Topics in Physical Science**

**- 0-4 cr.**

Occasional or special-purpose courses in physics, electronics, history or cultural aspects of science, on a level appropriate to the junior or senior student.

**PSC 4777 -**

**Advanced Topics in Physical Science**

**- 1-4 cr.**

Occasional or special-purpose courses in physics, electronics, history or cultural aspects of science, on a level appropriate to the junior or senior student.

**PSC 4999 -**

**Independent Study/Project in Physical Science**

**- 0-4 cr.**

Students desiring to improve knowledge or expertise in one of above categories may select projects for study in depth under guidance of a department member.

**Prerequisite Courses:**approval of a supervising faculty member.