# Course Descriptions

Listed below are the course descriptions for the selected subject.
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## MATHEMATICS

MATH 0100 -- Pre-Algebra,   3 credits  Common Course Outline
Prerequisite: Required score on math placement test

Review of the mathematical skills needed for the study of algebra as well as a brief introduction to algebra. Topics include the arithmetic of integers, fractions, decimals, and percents; applications of these arithmetic skills to problems involving measurement, percent, ratio, and proportion; and math study skills. The introduction to algebra consists of operations on signed numbers, algebraic expressions, solving linear equations and an introduction to graphing.

MATH 0230 -- Mathematical Foundations with Elementary Algebra,   5 credits  Common Course Outline
Prerequisites: Required score on math placement test

This course includes pre-algebra content centered on the mathematical skills needed for the study of algebra including the arithmetic of integers, fractions, decimals, and percents, and applications of these skills to problems involving measurement, percent, ratio, and proportionality. The elementary algebra content of the course prepares students to take MATH 0250, Math 1100, or Math 1114. This content includes properties of the real number system, simplifying algebraic expressions, properties of integer exponents, operations with polynomial expressions, methods for solving linear and quadratic equations, applications of these equations, introduction of sequences and series, mathematical modeling applications and using graphs to answer questions. Additional course content includes math study skills and STEM/Non-STEM math pathways exploration.

MATH 0240 -- Mathematical Concepts with Elementary Algebra,   5 credits  Common Course Outline
Prerequisites: MATH 0100 with a grade of C or better, or appropriate score on the math placement test

Recommended Skills, Abilities, or Coursework: This course is designed for persons who have good arithmetic skills and have had some high school algebra.

Prepares students to take Intermediate Algebra, Liberal Arts Mathematics or Introductory Statistics. The goal of this course is to provide prerequisite topics related to Liberal Arts mathematics and Introductory Statistics along with building the algebraic comprehension and skills needed for an Intermediate Algebra course. Topics include math study skills, STEM/Non-STEM math pathways; properties of the real number system; simplifying algebraic expressions; properties of integer exponents; operations on polynomial expressions; methods for solving linear and quadratic equations and proportions; applications of these equations; introduction of sequences and series; mathematical modeling applications and using graphs to answer questions.

MATH 0250 -- Intermediate Algebra,   5 credits  Common Course Outline
Prerequisites: MATH 0240 with a grade of C or better or appropriate score on math placement test

This course is a continuation of Math 0240 and prepares students to take Math 1200 or Math 1210. Topics include factoring, linear and quadratic functions; exponents; complex numbers; polynomial, rational and radical expressions; solutions of linear, quadratic, rational, absolute value, exponential, radical, and logarithmic equations; and inequalities.

MATH 1100 -- Mathematics for Liberal Arts,   3 credits  Common Course Outline
(MnTC Goal 4)

Prerequisite: MATH 0240 with a grade of C or better or appropriate score on math placement test

This course is designed for students intending to major in liberal arts areas such as English, the social sciences, foreign languages, art, music, etc. The course topics may include (but are not limited to): sets and counting, patterns and symmetry, data collection, probability, statistics, normal distributions, personal finance, voting methods, weighted voting and power, apportionment methods, sequences, mathematical modeling, and graph theory. Note: this course is not a prerequisite for any higher-level math courses.

MATH 1114 -- Introduction to Statistics,   4 credits  Common Course Outline
(MnTC Goal 4)

Prerequisite: MATH 0240 with a grade of C or better or appropriate score on math assessment test

Recommended Skills, Abilities, or Coursework:
1. Arithmetic skills with whole numbers, integers, fractions/ratios, and decimals.
2. Computational skills with percentages and decimals.
3. Algebraic skills with linear, quadratic, and rational expressions and equations.
4. Manipulative facility with square roots.
5. Facility with graphing straight lines from knowledge of the equation, slope/intercept, or point/intercept.

Introductory course in data description and analysis using graphical and numerical methods. Students will work with discrete and continuous random variables and their probability distributions with emphasis on the normal distribution. Topics include: experimental design and sampling methods; confidence intervals, sample size, and hypothesis testing for one and two population means or proportions; t and z tests, chi-square tests, analysis of variance (ANOVA), and linear regression; use of statistical software.

MATH 1121 -- Mathematics for Educational Arts,   4 credits  Common Course Outline
(MnTC Goal 4)

Prerequisites: MATH 0250 with a grade of C or better or appropriate score on math placement test

This course is about the nature of mathematics from a problem-solving approach using sets, relations, number systems, discrete mathematics, and basic algebra. The course explores the development of problem solving and decision making strategies using mathematical tools from arithmetic, algebra, and geometry. Skills to communicate and explain mathematical topics are also explored.

MATH 1189 -- Topics:,  Common Course Outline
This course has been developed as a potential permanent course. The course must follow all the same policies and procedures related to curriculum outlined by the college. It does not duplicate existing course offerings. Refer to course notes for specific course description.

MATH 1200 -- College Algebra,   3 credits  Common Course Outline
(MnTC Goal 4)

Prerequisites: Math 0250 with a grade of C or better or appropriate score on the math placement test

Topics include functions and function inverses; exponential and logarithmic functions; polynomial and simple rational functions; introduction to linear programming; systems of equations and inequalities; sequences and series; probability; and modeling. The completion of two years of high school algebra and one year of high school geometry is recommended.

MATH 1201 -- College Algebra II and Trigonometry,   4 credits  Common Course Outline
(Meets MnTC Goal 4)

Prerequisites: MATH 1200 with a grade C or better or appropriate score on math placement test

Topics covered are trigonometric and circular functions; trigonometric identities and equations; inverse trigonometric functions; rational functions; introduction to matrices and determinants; conics; parametric equations; polar coordinates; and modeling.

MATH 1210 -- Pre-Calculus,   5 credits  Common Course Outline
(MnTC Goal 4)

Prerequisites: Appropriate score on the math placement test or recommendation from your Math 0250 instructor

This course is intended to be a one-semester path to Calculus for students who have had at least three years of high school mathematics, including trigonometry. This course consists of material from Math 1200 and Math 1201. Topics include polynomial, rational, exponential, logarithmic, and trigonometric functions and their inverses; systems of equations and inequalities; matrices and determinants; trigonometric identities; equations and applications; parametric equations; polar coordinates; sequences and series; probability; conics and modeling. (Cannot be taken for credit if student has received credit for both Math 1200 and Math 1201.)

MATH 1310 -- Survey of Calculus,   3 credits  Common Course Outline
(MnTC Goal 4)

Prerequisite: MATH 1200 with a grade of C or better

Designed for students who need a one-semester survey course in calculus. Students intending to take the calculus sequence of MATH 1400 or MATH 1401 should not take this course. Topics included are functions; limits; differentiation of algebraic, exponential and logarithmic functions; integration with standard forms; and applications to management, social, and life sciences.

MATH 1400 -- Calculus I,   5 credits  Common Course Outline
(MnTC Goal 4)

Prerequisite: MATH 1201 or MATH 1210 with a grade of C or better or appropriate score on math placement test

Transfer course intended for bachelor programs in technology, engineering, mathematics, or science, including natural, physical, and social sciences. Topics include limits, derivatives (including trigonometric functions), continuity, applications of derivatives to related rates, optimization and graphing, simple differential equations, Riemann Sums, basic integration techniques, definite integral, and the Fundamental Theorem of Calculus. Students will become proficient with appropriate technology.

MATH 1401 -- Calculus II,   5 credits  Common Course Outline
(MnTC Goal 4)

Prerequisite: MATH 1400 with a grade of C or better

A continuation of Math 1400, this is a transfer course intended for Bachelor programs in technology, engineering, mathematics, or science, including natural, physical, and social sciences. Topics include the theory and techniques of integration, application problems involving integration, an introduction to differential equations, and infinite sequences and series, polar coordinates, and parametric curves.

MATH 2100 -- Discrete Mathematics,   4 credits  Common Course Outline
Prerequisite: MATH 1400 with a grade of C or better

(Cross-listed as CSCI 2100)

Intended for Math and/or Computer Science majors/minors. Topics include: logic, sets, functions, partitions and equivalence relations, binary operations, composition of functions, mathematical induction, combinatorics, matrix representations of graphs, isomorphisms of graphs, trees and spanning trees, recurrence relations, and generating functions. Applications include: Boolean algebra, algorithms and their efficiency, pigeon hole principle, and the halting problem.

MATH 2200 -- Linear Algebra,   4 credits  Common Course Outline
Prerequisite: MATH 1401 with a grade of C or better

Intended for students in the areas of engineering, sciences, or mathematics. This course serves these students with both practical applications of mathematics and as a bridge between lower level mathematics courses and higher level (often more theoretical) mathematics. Topics include matrix operations; systems of linear equations; Gaussian elimination; determinants; matrix inverses; vectors; vector spaces; subspaces; linear independence; linear transformations; matrix transformations; dimension; eigenvalues and eigenvectors; diagonalization; and orthogonality. Supplementary topics and technology-based assignments may vary.

MATH 2201 -- Introductory Linear Algebra,   2 credits  Common Course Outline
Prerequisite: MATH 1401 with a grade of C or better

Intended for students in the areas of engineering, sciences, or mathematics who only need an introduction to linear algebra. This course serves these students with both practical applications of mathematics and as a bridge between lower-level mathematics courses and higher-level mathematics courses that are often more theoretical. Topics include matrix operations, systems of linear equations, Gaussian elimination, determinants, matrix inverses, vectors, vector spaces, subspaces, linear independence, linear transformations, matrix transformations, dimension, eigenvalues, eigenvectors, and diagonalization.

MATH 2210 -- Differential Equations,   4 credits  Common Course Outline
Prerequisite: MATH 1401 with a grade of C or better

Intended for students in the areas of engineering, sciences, or mathematics. Topics include first and second order differential equations; existence and uniqueness of solutions; systems of linear equations; undetermined coefficients; variation of parameters; Laplace transforms; and numerical approximation of solutions. This course serves these students with both practical applications of mathematics and as a bridge between lower-level mathematics courses and higher-level (often more theoretical) mathematical courses.

MATH 2220 -- Multivariable Calculus and Vector Analysis,   5 credits  Common Course Outline
Prerequisite: MATH 1401 with a grade of C or better

Topics include vectors and analytic geometry in three dimensions, elementary calculus of vector-valued functions, elementary calculus of functions of several variables, multiple integration, vector calculus topics including Green's Theorem and Stokes' Theorem.

MATH 2230 -- Probability and Statistics,   4 credits  Common Course Outline
(MnTC Goal 4)

Prerequisite: MATH 1401 with a grade of C or better

Recommended Skills, Abilities, or Coursework:
1. Algebraic skills, including facility with exponential and logarithmic
functions.
2. Facility with limits, derivatives, maximum/minimum problems.
3. Basic techniques of integration for finding areas beneath curves.

This is a calculus-based course in the study of probability and statistics. Topics include descriptive statistics, general probability, probability distributions, sampling, descriptive statistics, normal and binomial distributions, interval estimation and hypothesis testing, chi-squared and t-tests, two-sample inference, analysis of variance, correlation and linear regression analysis. Students will also learn how to use a statistical software package. Concepts are introduced at more advanced level than in MATH 1114.

MATH 2299 -- Independent Study,  Common Course Outline
Independent Study allows a student to earn credit while participating in a supervised learning experience in a community-based or work setting. Students must have successfully completed two courses in the discipline in which they want to undertake independent study. Forms are available in the Educational Services Office. All arrangements must be made prior to registration for the semester in which the project is scheduled and must be approved by the appropriate Dean of Educational Services. In addition, a project outline must be approved by the instructor who will supervise the student's work.