# Course Descriptions

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- Syllabus Checklist - Requirements and Suggestions - College Arts and Sciences
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- Lower Division Course Syllabi

- Math Tutoring On Campus
- Learning Outcomes for Undergraduate Courses

**Courses marked** **with an** ****** **are only offered at Regional Campuses.**

**Basic Algebra** **Series**

- Fundamental Math to Basic Algebra Conversion chart
- Flowchart for the Basic Algebra classes and beyond

**00020 PRE-ALGEBRA (2)**

Properties of whole numbers, fractions, decimals, percents, signed numbers and order of operations, to a greater degree than in Basic Algebra I and Basic Algebra II. Mental math and elementary algebraic thinking skills are emphasized and use of calculator is not allowed. Hours not counted toward graduation. **Prerequisite:** none.

**00021** **BASIC AGEBRA** **I (2)**

Includes operations on integers, fractions, decimals and percents, properties of real numbers. Introduction to variables, first degree equations and problem-solving with formulas. Equations and inequalities in one variable, linear equations, rate of change and slope, graphing in the Cartesian plane. Hours do not count toward graduation. **Prerequisite or corequisite:** minimum C (2.0) grade in MATH 00020; or 0-29 on ALEKS level one assessment; or 0-14 on ALEKS level two assessment; or 10-24 on ALEKS singular assessment.

**00022** **BASIC AGEBRA** **II (2)**

Introduction to functions, systems of linear equations, exponents, polynomial operations, scientific notation. Factoring polynomials, solving quadratics by factoring, radicals and rational exponents. Hours not counted toward graduation. **Prerequisite or corequisite:** minimum C (2.0) grade in MATH 00021; or 30-39 on ALEKS level one assessment; or 25-34 on ALEKS singular assessment.

**00023** **BASIC AGEBRA** **III (2)**

Zeros of functions, rational expressions and equations, problem-solving with rational expressions, intermediate factoring techniques. Quadratics: functions, graphs, equations, inequalities, "quadratic type" equations and problem-solving. **Prerequisite or corequisite:** minimum C (2.0) grade in MATH 10006 or in MATH 00022; or 40-100 on ALEKS level one assessment; or 15-29 on ALEKS level two assessment; or 35-44 on ALEKS singular assessment.

**00024** **BASIC AGEBRA** **IV (2)**

Advanced factoring techniques, rational functions, radical equations, absolute value equations and inequalities. Exponential and logarithmic functions: introduction, graphing, problem-solving. **Prerequisite or corequisite:** minimum C (2.0) grade in MATH 00023; or 30-39 on ALEKS level two assessment; or 45-54 on ALEKS singular assessment.

**10041 ELEMENTARY PROBABILITY AND STATISTICS (3**) ** ** **MATH 10041 Syllabus**

Descriptive statistics, probability concepts, binomial and normal distributions. Sampling, estimation, hypothesis testing. Analysis of paired data, linear models and correlation. Prerequisite: minimum C (2.0) grade in MATH 10007 or MATH 00023; or 30-39 on ALEKS level two assessment; or 45-54 on ALEKS singular assessment.

**11008 EXPLORATIONS IN MODERN MATHEMATICS (3) MATH 11008 Syllabus
**Topics from various branches of mathematics will be chosen to introduce the student to the wide varieties of ways in which mathematics affects everyday life. Prerequisite: minimum C (2.0) grade in MATH 10007 or MATH 00023; or 30-39 on ALEKS level two assessment; or 45-54 on ALEKS singular assessment.

**11009 MODELING ALGEBRA (4) MATH 11009 Syllabus
**Study of algebra arising in the context of real-world applications, including linear, polynomial, exponential and logarithmic models. Intended for students not planning to take calculus. No graduation credit for this course for students who have already passed MATH 11010. Prerequisite: minimum C (2.0) grade in MATH 10007 or MATH 00023; or 30-39 on ALEKS level two assessment; or 45-54 on ALEKS singular assessment.

**11010 ALGEBRA FOR CALCULUS MATH 11010 Syllabus
**Study of elementary functions and graphs, including polynomial, exponential and logarithmic functions; complex numbers; binomial theorem. No credit earned for this course if student earned credit for MATH 11011 or 12001. Prerequisite: minimum C (2.0) grade in MATH 10007 or MATH 00024; or 40-49 on ALEKS level two assessment; or 55-66 on ALEKS singular assessment.

**11012 INTUITIVE CALCULUS (3) MATH 11012 Syllabus
**Designed to give an overview of differential and integral calculus to business and life-science majors. Does not include trigonometric functions. No credit earned for this course if student earned credit for MATH 12002. Prerequisite: minimum C (2.0) grade in MATH 11010; or 50-69 on ALEKS level two assessment; or 67-77 on ALEKS singular assessment.

**11022 TRIGONOMETRY (3) MATH 11022 Syllabus
**Solution of triangles, trigonometric equations and identities. Prerequisite: minimum C (2.0) grade in MATH 11010; or 50-69 on ALEKS level two assessment; or 67-77 on ALEKS singular assessment.

**12001 ALGEBRA-TRIGONOMETRY (5) MATH 12001 Syllabus
** A Combination of MATH 11010 and MATH 11022. Designed for students who want to finish their algebra and trigonometry requirement in one semester. Prerequisite: minimum B (3.0) grade in MATH 10024; or 67-77 on ALEKS singular assessment.

**12002 ANALYTIC GEOMETRY AND CALCULUS I (5) MATH 12002 Syllabus
**Concepts of limit, continuity and derivative, and the indefinite and definite integral for functions of one real variable. Maximization, related rates, fundamental theorem of calculus. No credit earned for this course if student earned credit for MATH 12011 or 12012. Prerequisite: minimum C (2.0) grade in MATH 11010 and MATH 11022; or 70-100 on ALEKS level two assessment; or 78-100 on ALEKS singular assessment.

**12003 ANALYTIC GEOMETRY AND CALCULUS II (5) MATH 12003 Syllabus
**Continued study of techniques and applications of integration; trigonometric, logarithmic and exponential functions; polar coordinates; vectors; parametric equations; sequences and series. Prerequisite: MATH 12002 or MATH 12012.

**12011 CALCULUS WITH PRECALCULUS I (3) MATH 12011 Syllabus
**Introduction to differential calculus with a review of algebra and trigonometry. Includes exponents, factoring, functions, graphs, tangent lines, limits, continuity, derivatives and related rates. No credit earned for this course if student earned credit for MATH 12002. Prerequisite: minimum C (2.0) grade in MATH 11010 and MATH 11022; or 50-69 on ALEKS level two assessment; or 67-77 on ALEKS singular assessment.

**12012 CALCULUS WITH PRECALCULUS II (3) MATH 12012 Syllabus
**Development of integral calculus and continued study of differential calculus. Includes curve sketching optimization fundamental theorem of calculus areas between curves, exponential and logarithmic functions. No credit earned for this course if student earned credit for MATH 12002. Prerequisite: MATH 12011.

**12021 CALCULUS FOR LIFE SCIENCES (4) MATH 12021 Syllabus
**Differential and integral calculus using examples and problems in life sciences. Prerequisite: Integrated life science (ILS) major; and/or 70-100 on ALEKS level two assessment; and/or 78-100 on ALEKS singular assessment.

**12022 PROBABILITY AND STATISTICS FOR LIFE SCIENCES (3) MATH 12022 Syllabus
**Probability and statistics with applications in medical and biological sciences. Prerequisite: MATH 12002 or MATH 12012 or MATH 12021.

**14001 BASIC MATHEMATICAL CONCEPTS I (4) MATH 14001 Syllabus
**Development of the real number system and its sub-systems, numeration systems, logic, place value, modular arithmetic, sets, some number theory and algebra concepts, problem solving.

**Prerequisite**: minimum C (2.0) in any math course 10023 or higher; or ALEKS placement score 45-54.

**14002 BASIC MATHEMATICAL CONCEPTS II (4) MATH 14002 Syllabus
**Basic concepts of probability, statistics and geometry. Prerequisite: MATH 14001.

********19001 TECHNICAL MATHEMATICS I (4)**********
**Introduction to geometry, algebra and trigonometry. For students in the engineering technologies. Prerequisite: Special approval.

********19002 TECHNICAL MATHEMATICS II (4)**********
**Continuation of MATH 19001. Emphasizes advanced topics in algebra and trigonometry, analytic geometry, derivatives and integrals. Prerequisite: MATH 19001.

**19099 FIELD EXPERIENCE IN MATHEMATICS INSTRUCTION (1)
**Learning through tutoring. A supervised lab experience in providing explanations of mathematical concepts. May be repeated in a different area. Prerequisite: Special approval.

**20095 (001-020) ALGEBRA FOR CALCULUS PLUS Plus (4 credit hours)**. This course is a combination of 00024 and 11010 for 4 credits, with access for students with ALEKS 45 or higher. (Permanent course to be submitted for Fall 15)

**20095 (021-040) MODELING ALGEBRA PLUS (5 credit hours)**. This course is a combination of 00023 and 11009 for 5 credits, with access for students with ALEKS 35 or higher. (Permanent course to be submitted for Fall 15).

**20095 (041-060) ALGEBRA FOR CALCULUS STRETCH I (3 credit hours)** First of a 2 semester sequence combining 00023, 00024, 11010 for 3 credits each, with access for students with ALEKS 35 or higher, lower than ALEKS 35 must have ACT 22 or higher and receive extra support in the form of mandated tutoring. (Permanent course to be submitted for Fall 15).(The mandated tutoring students are those who score 22 or higher on ACT but place into 00020, 00021, or 00022).

**21001 LINEAR ALGEBRA WITH APPLICATIONS (3) MATH 21001 Syllabus
**Systems of linear equations and the associated matrix operations, linear transformations, vector spaces, bases, eigenvectors. Prerequisite: MATH 11012 or MATH 12002.

********21003 INTRODUCTION TO SYSTEMS ANALYSIS AND DATA COMMUNICATIONS (3)**********
**Background in the topic of systems analysis, design development and implementation including an overview of teleprocessing. Prerequisite: MIS 24080.

********21092 COMPUTER PRACTICUM (2)**********
**Supervised work experience in a computer installation. Prerequisite: None.

**22005 ANALYTIC GEOMETRY AND CALCULUS III (3) MATH 22005 Syllabus
**Study of functions of several variables, including partial derivatives and multiple integrals. Prerequisite: MATH 12003.

**23022 DISCRETE STRUCTURES FOR COMPUTER SCIENCE (3)
**Discrete structures for computer scientists with a focus on: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, applications and modeling. Specific topics include logic, sets, functions, relations, algorithms, proof techniques, counting, graphs, trees, Boolean algebra, grammars and languages. No credit for MATH 31011. Prerequisite: CS 10051 and a grade of C (2.0) or better in MATH 11010; or a Compass Algebra score of 55 or better and either SAT Math score of 540 or better or ACT Math score 23 or better.

**30011 BASIC PROBABILITY AND STATISTICS (3)
**Analysis and representation of data. Controlled experiments and observations. Measurement errors. Correlation and regression. Sampling. Probability models and tests of models. Inference. Prerequisite: Grade of C (2.0) or better in MATH 11010.

**30055 MATHEMATICAL THEORY OF INTEREST (3)
**A calculus-based introduction to the mathematics of finance. Limited to deterministic analysis of interest rates annuities bonds and immunization. Emphasizes the mathematical theory of the subject matter. Prerequisite: MATH 12003.

**31011 DISCRETE MATHEMATICS (3)
**Discrete mathematical techniques and structures including finite set theory, graph theory, propositional calculus, combinatorics and discrete probability. Formal methodology and proof techniques. No credit for MATH 23022. Prerequisite: MATH 12002. Pre/corequisite: MATH 21001.

**31045 FORMAL LOGIC (3)
**Study of first order predicate calculus with identity and function symbols. Prerequisite: None.

**32044 INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS (3)
**An introduction to ordinary differential equations and applications. Topics include solution methods, series solutions and singular points. Laplace transforms and linear systems. Applications include population dynamics, forced oscillations and resonance. Prerequisites: MATH 21001 and MATH 22005.

**32051 MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES I (4)
**Mathematics background beyond Calculus I and II for upper-division courses in the physical sciences. Topics include complex numbers and arithmetic, linear algebra, partial differentiation and multiple integrals. Prerequisite: MATH 12003.

**32052 MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES II (4)**

Additional mathematics background for upper-division courses in the physical sciences. Topics include vector analysis, Fourier series and transforms ordinary differential equations and partial differential equations. Prerequisites: MATH 32051 or MATH 21001 and MATH 22005.

**34001 FUNDAMENTAL CONCEPTS OF ALGEBRA (3)
**Professionalized course in algebra for prospective secondary teachers. Postulational development of number system of algebra; other systems, related topics, applications. Prerequisite: MATH 12002.

**34002 FUNDAMENTAL CONCEPTS OF GEOMETRY (3)
**Professionalized course in geometry for secondary school teachers. Origin and development of the geometry of Euclid with modern refinements, topics, approaches. Other geometries, applications. Prerequisite: MATH 12002.

**40011 INTRODUCTION TO PROBABILITY THEORY AND APPLICATIONS (3)
**Permutations and combinations, discrete and continuous distributions, random variables, conditional probabilities, Baye's formula, mathematical expectation, law of large numbers, normal approximations, basic limit theorems. Prerequisite: MATH 12003.

**40012 INTRODUCTION TO STATISTICAL CONCEPTS (3)
**Sample spaces, continuous distributions, sampling distributions, point and interval estimation, hypothesis testing, types of error, level and power of tests, sequential and nonparametric methods. Prerequisite: MATH 40011.

**40022 LINEAR MODELS AND STATISTICAL ANALYSIS (3)
**Regression model, multivariate normal distribution, point and interval estimates, Gauss-Markov Theorem, correlation and regression, tests of hypotheses, applications. Prerequisite: MATH 21001 and MATH 40012.

**40031 BASIC NONPARAMETRIC STATISTICS (3)
**Rank tests for different kinds of hypothesis, large sample theory, efficiency comparisons, tests of Kolmogorov-Smirnov type. Prerequisite: MATH 40012

**40041 STATISTICAL METHODS FOR EXPERIMENTS (3)
**Comparison of two groups, t- and F-statistics; ANOVA, one-way and multiway layouts, randomization blocking. Linear regression, correlation and analysis of covariance (ANCOVA). Repeated measures analysis of variance. Prerequisite: MATH 30011.

**40042 SAMPLING THEORY (3)
**This introductory course provides the methodology for the design and analysis of sampling and surveying studies. Simple random, stratified, cluster, PPS and two- stage sampling techniques. Linear, ratio and regression estimators. Prerequisite: MATH 30011.

**40051 TOPICS IN PROBABILITY THEORY AND STOCHASTIC PROCESSES (3)
**Topics from conditional expectations, Markov chains, Markov processes, Brownian motion and Martingales and their applications to stochastic calculus. Prerequisite: MATH 40011.

**40055 ACTUARIAL MATHEMATICS I (4)**

Topics from survival models, stochastic analysis of annuities and life insurance and casualty models. Prerequisite: MATH 30055 and MATH 40011.

**40056 ACTUARIAL MATHEMATICS II (4)**

Benefit premiums, benefit reserves and their analysis, decrement models, joint survivorship, risk models. Prerequisite: MATH 40055.

**40091 SEMINAR IN ACTUARIAL MATHEMATICS (2)
**Seminar course designed to prepare students for the society of actuaries examination on actuarial mathematics. Prerequisite: MATH 40056.

**40093 VARIABLE TITLE WORKSHOP IN MATHEMATICS (1-6)
**Studies special topics in mathematics. Not acceptable for credit toward a major or minor in math without approval of student's adviser. S u/graded. Prerequisite: Permission.

**41001 INTRODUCTION TO MODERN ALGEBRA I (3)
**Basic properties of groups, subgroups, factor groups. Basic properties of rings, integral domains, and homomorphisms. Prerequisite: MATH 21001 and MATH 22005.

**41002 INTRODUCTION TO MODERN ALGEBRA II (3)
**A continuation of MATH 41001, emphasizing properties of rings, their ideals, polynomial ring extensions, fields, finite degree extensions, roots of polynomials, constructability. Prerequisite: MATH 41001.

**41012 FINITE MATHEMATICS (3)
**A continuation of Discrete Math, emphasizing combinatorial techniques, graph applications in algorithms, finite algebra, number theory and probability. Covers useful math for CS majors. Prerequisite: CS 31011 or MATH 31011.

**41021 THEORY OF MATRICES (3)
**A rigorous study of the topics introduced in matrix algebra. Topics included are vector space preliminaries, canonical forms of matrices, diagonalizability criteria. Prerequisite: MATH 21001 and MATH 22005.

**41045 METALOGIC (3)
**May be counted toward B.A. or B.S. mathematics major. Consideration of various metatheorems, including soundness and completeness of propositional and predicate calculus, undecidability of predicate calculus and incompleteness of the theory of arithmetic. Prerequisite: PHIL 31045.

**42001 INTRODUCTION TO ANALYSIS I (3)
**Topics include basic structure of the real numbers, Cauchy sequences, convergence, completeness of the real numbers, continuity, differentiation and Riemann integration. Prerequisite: MATH 21001 and MATH 22005.

**42002 INTRODUCTION TO ANALYSIS II (3)
**Topics include further development of integration theory, infinite series, uniform convergence, several variable calculus and metric spaces. Prerequisite: MATH 42001.

**42011 MATHEMATICAL OPTIMIZATION (3)
**Analytic and numerical techniques for location of extreme points of functions and calculus of variations. Both constrained and unconstrained problems are considered. Prerequisite: MATH 21001 and MATH 22005.

**42021 GRAPH THEORY AND COMBINATORICS (3)
**Fundamentals and applications of combinatorial mathematics. Topics include traversability, colorability, networks, inclusion and exclusion, matching and designs. Prerequisite: MATH 21001 and MATH 12003.

**42024 NUMBERS AND GAMES (3)
**The study of partisan and impartial combinatorial games; games as numbers; Grundy-Sprague theory. Prerequisite: MATH 21001.

**42031 MATHEMATICAL MODELS AND DYNAMICAL SYSTEMS (3)
**Formulation and analysis of mathematical models for a variety of phenomena. Mathematical methods from optimization dynamical systems and probability are developed and applied. Modern software tools are utilized. Prerequisite: MATH 32044 or 32052.

**42041 ADVANCED CALCULUS (3)
**The calculus and applications of scalar and vector functions of several variables. Vector differential and integral calculus. Applications to field theories, electricity and magnetism, and fluid flow. Prerequisite: MATH 21001 and MATH 22005.

**42045 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS (3)
**An introduction to Fourier series, Fourier transforms and partial differential equations. Wave, heat and potential equations of mathematical physics. Additional topics include Green's functions and the Method of Characteristics for wave equations. Prerequisite: MATH 32044.

**42048 INTRODUCTION TO COMPLEX VARIABLES (3)
**Algebra of complex numbers, analytic functions, mappings, Cauchy integral theory, residue theory and applications. Prerequisite: MATH 22005.

**42091 SEMINAR:MODELING PROJECTS (3)
**Individual and small-group projects concerned with the formulation and analysis of mathematical models in a variety of areas. Written and oral reports are required. Prerequisite: MATH 42031.

**42201 NUMERICAL COMPUTING I (3)
**An introduction to numerical methods and software for solving many common scientific computing problems. Linear systems, least-squares data fitting, nonlinear equations and systems, and optimization problems. Prerequisite: MATH 12003; and MATH 21001 or MATH 32051; and CS 10061 or CS 23021.

**42202 NUMERICAL COMPUTING II (3)
**A continuation of MATH 42201. Topics include interpolation, numerical differentiation and integration, and numerical solution of ordinary differential equations. Prerequisite: MATH 42201; and MATH 32044 or 32052.

**45011 DIFFERENTIAL GEOMETRY (3)
**Analytic and metric differential geometry of curves and surfaces. Prerequisite: MATH 22005.

**45021 EUCLIDEAN GEOMETRY (3)
**Geometry of Euclid extended to advanced topics of the triangle, quadrilaterals and circles: cross-ratio, groups, constructions, geometric generalizations; inversion. Prerequisite: MATH 21001 or special approval of instructor.

**45022 LINEAR GEOMETRY (3)
**Using transformations as a tool to study geometry and to differentiate between different kinds of geometry. Linear algebra methods applied to geometry. Prerequisite: MATH 21001.

**46001 ELEMENTARY TOPOLOGY (3)
**Metric spaces, introduction to topological spaces, separation axioms. Prerequisite: MATH 22005.

**47001 MATHEMATICAL LOGIC AND SET THEORY (3)
**Axiomatic set theory, relations development of real numbers cardinal numbers axiom of choice. Prerequisite: Permission.

**47011 THEORY OF NUMBERS (3)
**Divisibility properties of the integers, prime numbers, congruences, quadratic reciprocity, Diophantine equations, number theoretic functions, simple continued fractions, rational approximations. Prerequisite: MATH 12003.

**47021 HISTORY OF MATHEMATICS (3)
**Survey from Babylonian and Egyptian mathematics to 20th century mathematics with emphasis on the development of algebra, geometry, calculus, number theory. Prerequisite: 3 hours of mathematics beyond MATH 22005.

**49995 SELECTED TOPICS IN MATHEMATICS AND ITS APPLICATIONS (1-4)
**(repeated registration permitted) various special courses will be announced in the schedule of classes under this course number with different section numbers. Prerequisite: Permission.

**49996 INDIVIDUAL STUDY (1-4)
**Prerequisite: Permission.

**49998 RESEARCH (1-15)
**Prerequisite: Permission.

**Courses marked with an** ****** **are only offered only at Regional Campuses.**

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