Mathematics

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.

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.

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.

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.

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.

Limits, continuity and fundamental theory of differentiation, symbolic and numerical calculations of derivatives, applications of derivatives; definite integrals and Riemann sums.

Study of numerical integration, applications of definite integrals, improper integrals, sequences and infinite series, basic ideas and methods for solving differential equations.

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.

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.

Topics.

Foundations of Euclidean geometry, solid geometry; introductions to non-Euclidean geometry; spherical geometry. Course includes dynamic geometry investigations using appropriate software.

Topics include functions of several variables, gradients, partial derivatives and multiple integrals, vector fields, Green's and Stoke's theorems, and applications.

Further study of systems of linear equations, matrices and determinants, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, diagonalization.

Introduction to the theory of differential equations, varied methods to solve linear, nonlinear equations, quantitative analysis of solutions of equations.

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.

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.

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.

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.

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.

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.

Internship in Mathematics.

Concentrated study of various subject areas.

Research projects for upper-division students.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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

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.