# MATH - Mathematics

College of Natural and Health Sciences

School of Mathematical Sciences

- Contact (970) 351.2820
- www.unco.edu/NHS/mathsci

Please note: All students are required to complete a web-based placement assessment called ALEKS to determine readiness for entry-level mathematics and statistics courses. Entry-level mathematics and statistics courses that require the ALEKS assessment include MATH 023, MATH 120, MATH 124, MATH 125, MATH 127, MATH 131, MATH 171, and STAT 150. More information on ALEKS and a link to the assessment can be found at http://www.unco.edu/nhs/mathsci/undergrad/placement/placement.html.

## MATH 023 Intermediate Algebra

Elementary concepts of algebra including quadratic equations, the function concept and systems of linear equations. This basic skills course does not count for university credit nor in the GPA.

## MATH 102 Success in the Mathematical Sciences

Majors only; freshman only. An introduction to academic life at UNC, the mathematical sciences majors, and careers in the mathematical sciences for incoming freshmen. S/U graded. Non-repeatable.

## MATH 120 Mathematics and Liberal Arts

Prerequisite: Minimum of one full year of high school algebra with a grade of C or better (C- is not acceptable). Nonmajors only. Learn about several topics in mathematics through intuitive presentation to help those who want to know more about mathematics. Not open to mathematics majors and minors. (LAC, gtP)

## MATH 123 Supplemental Algebra

Co-requisite: MATH 124. Provides supplemental academic support for students enrolled in College Algebra (MATH 124) including content review and study skills. Required course based on the math placement index. S/U graded.

## MATH 124 College Algebra

Prerequisites: A satisfactory score on the math placement index and either two years of high school algebra with a grade of C or better (C- is not acceptable) or the equivalent. Topics covered in this course include linear, quadratic, exponential and logarithmic functions, matrices, theory of equations. (LAC, gtP)

## MATH 125 Plane Trigonometry

Prerequisite: MATH 124 or equivalent High School course with grade of C or better (C- is not acceptable). Study circular functions and their applications, inverse trigonometric functions and identities and cover complex numbers through DeMoivre's Theorem. (LAC, gtP)

## MATH 127 Elementary Functions

Prerequisite: Full year of modern, second year high school algebra with the grade of B or better. Develop those skills required in calculus, including polynomial functions, exponential and logarithmic functions, trigonometric functions, vectors, analytic geometry and polar coordinates. (LAC, gtP)

## MATH 130 Supplemental Calculus

Co-requisite: MATH 131 or MATH 171. Provides support for students taking Calculus I by reviewing and exploring important prerequisite concepts required for calculus in a timely manner. Topics include relevant areas of algebra, trigonometry and pre-calculus. Repeatable, make be taken two times.

## MATH 131 Calculus I

Prerequisites: Satisfactory score on the mathematics placement index, and either high school mathematics up to and including trigonometry with a grade of B or better (B-is not acceptable) or college-level trigonometry or elementary functions with a grade of C or better (C- is not acceptable). Credit allowed for only one of MATH 131 and MATH 171. First course in a three course sequence in calculus. Differentiation and related concepts, applications of derivatives, including exponential, logarithmic and trigonometric functions. (LAC, gtP)

## MATH 132 Calculus II

Prerequisite: MATH 131 with the grade of C or better (C- is not acceptable). Second course in three course sequence in calculus. Integration and applications of integration, sequences and series. (LAC, gtP)

## MATH 171 Calculus I for Life Sciences

Prerequisite: A satisfactory score on the mathematics placement index, and either high school mathematics up to and including trigonometry with a grade of B or better (B- is not acceptable) or college-level trigonometry or elementary functions with grade of C or better (C- is not acceptable). Credit allowed for only one of MATH 131 and MATH 171. Differentiation and related concepts, applications of derivatives, including exponential. logarithmic and trigonometric functions. Introduction to integration. Emphasis on applications to the life sciences. (LAC, gtP)

## MATH 176 Topics in Calculus

Prerequisite: MATH 124 with a grade of "C" or better (C- is not acceptable); or an ACT score of 26 or higher in mathematics, or an SAT math score of 560 or higher prior to March 2016 or an SAT score of 580 or higher after March 2016. Techniques and applications of differential and integral calculus with an emphasis on applications to economics and business.

## MATH 181 Fundamentals of Mathematics I: Number and Operations

First of three courses designed for prospective elementary teachers. Emphasizes the real number system and arithmetic operations. Explorations focus on mathematical structures and subsets of real numbers, via patterns, relationships, and properties. Content presented using problem solving and exploration. Course fee required. (LAC, gtP)

## MATH 182 Fundamental Mathematics II: Algebra, Probability and Data Analysis

Prerequisite: MATH 181 with C or better or MATH 131 with C or better. Second of three courses designed for prospective elementary teachers. Emphasizes algebra, probability, and data analysis. Explorations focus on representing, analyzing, generalizing, formalizing, and communicating patterns and probabilities. Course fee required. (LAC, gtP)

## MATH 185 Number Sense and Algebra

Emphasizes development of algebraic reasoning in conjunction with arithmetic operations. Explorations focus on mathematical structures and operations via implementation of various concrete and abstract models, pattern analysis, relationships, and properties. This course is designed for prospective elementary teachers in the mathematics concentration. (LAC)

## MATH 186 Elements of Calculus

Prerequisite(s): MATH 185 or both MATH 181 and MATH 182 with a grade of "C" or better (C- is not acceptable). This course emphasizes the development of functional reasoning in conjunction with elementary calculus concepts. Explorations focus on functions, limits, structure of the real numbers, continuity, slope and integration concepts. This course is designed for prospective elementary teachers in the mathematics track. (LAC)

## MATH 221 Elementary Linear Algebra

Prerequisite: MATH 132 with the grade of C or better (C- is not acceptable). Vector spaces, linear transformations, matrices, determinants, eigenvalues and eigenvectors, applications.

## MATH 228 Discrete Mathematics

Prerequisite: MATH 131 with the grade of C or better (C- is not acceptable). A survey course of non-calculus based mathematics used extensively in computer science and other disciplines. Study sets, types of proofs, logic, recursion and related topics.

## MATH 233 Calculus III

Prerequisite: MATH 132 with the grade of C or better (C- is not acceptable). Third course in a three course sequence in calculus. Differentiation and integration of functions of several variables, vector functions, parametric equations, Green's Theorem.

## MATH 283 Fundamental Mathematics III: Geometry and Measurement

Prerequisite: MATH 182 or MATH 185 with grade of C or better (C- is not acceptable). Third of three courses designed for prospective elementary teachers. Emphasizes development of spatial reasoning in geometry and measurement. Explorations focus on two- and three dimensional shapes, their properties, measurements, constructions, and transformations. Course fee required.

## MATH 286 Elements of Discrete Mathematics

Prerequisite(s): MATH 186 or MATH 131 with a grade of "C" or better (C- is not acceptable). This course focuses on the topics in Discrete Mathematics that are most fundamental for Elementary and Middle School teachers. Topics include sequences, graph theory, set theory, counting methods and probability. This course is designed for prospective elementary teachers in the mathematics track.

## MATH 317 Mathematical Foundations for Teachers

Prerequisite: MATH 233 with a grade of "C" or better (C- is not acceptable). Focus is on depth of understanding and ability to explain models and concepts involving number operations, fractions, bases, ratio and proportion, functions, structure of the real and rational numbers.

## MATH 321 Introduction to Abstract Algebra I

Prerequisites: MATH 221 and MATH 228 with the grade of C or better (C- is not acceptable). An introduction to abstract algebra. Topics will include: basic number theory, group theory, geometrical connections and mappings.

## MATH 322 Introduction to Abstract Algebra II

Prerequisites: MATH 321 with a grade of C or better (C- is not acceptable). A continuation of MATH 321. Topics will include: rings, integral domains, fields and Galois theory.

## MATH 335 Differential Equations I

Prerequisite: MATH 233 with the grade of C or better (C- is not acceptable). Study the theory and solutions of ordinary differential equations including applications.

## MATH 336 Differential Equations II

Prerequisite: MATH 335 with the grade of C or better (C- is not acceptable). Continuation of MATH 335. The existence and uniqueness theory, systems of equations, boundary value problems and an introduction to partial differential equations.

## MATH 341 Introduction to Modern Geometry I

Prerequisites: MATH 228 or MATH 286 with the grade of C or better (C- is not acceptable). Explores Euclidean and non-Euclidean geometries from multiple perspectives, with an emphasis on developing problem solving, communication, and logical reasoning skills.

## MATH 342 Introduction to Modern Geometry II

Prerequisites: MATH 221, MATH 228 and MATH 341 with a grade of C or better (C- is not acceptable), or consent of instructor. Continuation of Math 341. This course will continue the study of the foundations of geometry, exploring Euclidean and non-Euclidean geometries.

## MATH 350 Elementary Probability Theory

Prerequisite or concurrent enrollment in MATH 132. An introduction to probability. Topics include descriptive techniques, regression counting techniques, probability random variables, probability distributions, mathematical expectations, moment generating functions, transformations, point estimation, confidence intervals and hypothesis testing.

## MATH 351 Elementary Statistics Theory

Prerequisite: MATH 350; MATH 233 (or concurrent enrollment) with a grade of C or better (C- is not acceptable). A continuation of MATH 350. Learn about jointly distributed random variables, central limit theorem, sampling distributions, properties of estimation, confidence intervals and tests of hypothesis.

## MATH 375 Elementary Numerical Analysis

Prerequisites: MATH 221 with the grade of C or better (C- is not acceptable), MATH 233 and ability to program. Numerical solutions of equations and systems of equations; interpolation and approximation; numerical differentiation and integration; numerical solutions of differential equations.

## MATH 386 Problem Solving

Prerequisite: MATH 286 or MATH 228 with a grade of "C" or better (C- is not acceptable).This course focuses on Mathematical Problem Solving for future elementary and middle school teachers. Emphasis is on problems that require fundamental concepts from a variety of mathematical topics and levels. This course is designed for prospective elementary teachers in the mathematics track.

## MATH 391 Introduction to Number Theory

Prerequisites: MATH 228 or MATH 286 with the grade of "C" or better (C- is not acceptable. Topics will include basic properties of the Natural Numbers, prime numbers, divisibility, factorization, congruences, Euler's phi function, introduction to Diophantine Equations and some group theory.

## MATH 395 Topics in Mathematics for Teachers

Prerequisites: MATH 182, MATH 228. Emphasis will be on problem solving skills, reasonableness of answers, using calculators and computers and on problem posing.

## MATH 422 Directed Studies

Individualized investigation under the direct supervision of a faculty member. (Minimum of 37.5 clock hours required per credit hour.) Repeatable, maximum concurrent enrollment is two times.

## MATH 431 Basic Analysis I

Prerequisite: MATH 233 with grade of C or better (C- is not acceptable). Sequence of two courses to extend studies of calculus and analysis into the mathematical rigor and logic of analysis. Includes: real numbers, sequences, topology, limits, continuity, differentiation, series and integration.

## MATH 432 Basic Analysis II

## MATH 437 Mathematical Modeling

Prerequisites: MATH 221 and MATH 233 with a grade of C or better (C- is not acceptable). Use mathematical tools to develop models of practical problems. Emphasize development, verification and interpretation of models and communication of results.

## MATH 460 Introduction to Complex Analysis

Prerequisite: MATH 233 with a grade of C or better (C- is not acceptable). First course in complex variables, especially for potential calculus teachers. After preliminaries, proceed directly to power series, Laurent's series, contour integration, residue theory, polynomials and rational function.

## MATH 464 Introduction to History of Mathematics

Prerequisites: MATH 221, MATH 228, MATH 341. Junior or above in Mathematics. Survey of mathematical conceptual development and the people involved from antiquity to the present, including pedagogical applications, content connections, and use of reference resources.

## MATH 495 Topics in Mathematics

Consent of instructor. Surveys topics in areas such as geometry, analysis, algebra, statistics, numerical analysis, topology and number theory not in existing courses, which reflect specific interests of instructors and students. Repeatable, under different subtitles.