MATH 0080 -- Principles of Mathematics, credits Common Course Outline This course is designed to support students' development of numeracy understanding and skills. Topics include the arithmetic of real numbers, linear relationships, and graphical representations of quantitative information. The class integrates strategies for navigating college mathematics including technology skills, time management, effective communication, and independent study skills. Successful completion of the course satisfies the prerequisites for enrollment in Math 0230 or Math 0240 at Anoka-Ramsey Community College. The course includes three hours of instructional time, and two additional hours of supported active learning time described in the course schedule. The supported learning hours may be completed in the classroom during scheduled times, or asynchronously through online learning platforms. MATH 0230 -- Mathematical Foundations with Elementary Algebra, 5 credits Common Course Outline Prerequisites: Math 0080 with a passing grade, or appropriate score on math placement testRecommended Skills, Abilities, or Coursework: This course is designed for students who have had some high school algebra.This course emphasizes the mathematical concepts and skills that prepare students to take Intermediate Algebra, Mathematics for Liberal Arts, or Introduction to Statistics. Topics include properties of the real number system, simplifying algebraic expressions, operations with polynomial expressions, methods for solving linear and quadratic equations and proportions, data displays and measures of central tendency, interpretations of graphs, mathematical modeling, STEM and Non-STEM math pathways, and mathematical study skills. The course includes five hours of instructional time, and two additional hours of supported active learning time designed to support the development of arithmetic and prealgebra understanding that underpins the content of the course. MATH 0240 -- Mathematical Concepts with Elementary Algebra, 5 credits Common Course Outline Prerequisites: MATH 0080 with a passing grade, or appropriate score on the math placement testRecommended Skills, Abilities, or Coursework: This course is designed for persons who have good arithmetic skills and have had some high school algebra.This course emphasizes the mathematical concepts and skills that prepare students to take Intermediate Algebra, Mathematics for Liberal Arts, or Introduction to Statistics. Topics include properties of the real number system, simplifying algebraic expressions, operations with polynomial expressions, methods for solving linear and quadratic equations and proportions, data displays and measures of central tendency, interpretations of graphs, mathematical modeling, STEM and Non-STEM math pathways, and mathematical study skills. MATH 0250 -- Intermediate Algebra, 5 credits Common Course Outline Prerequisites (must have a grade of C or better): MATH 0230 or MATH 0240 with a grade of C or better, or appropriate score on math placement testThis course is a continuation of MATH 0230 or MATH 0240 and prepares students to take 1200 or 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) Prerequisites (must have a grade of C or better): MATH 0230 or MATH 0240 with a grade of C or better, or appropriate score on math placement testThis 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) Prerequisites (must have a grade of C or better): MATH 0230 or MATH 0240 with a grade of C or better, or appropriate score on math placement testRecommended 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 testTopics 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 testTopics 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 instructorThis 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 testTransfer 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 betterA 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 betterIntended 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 betterTopics 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.