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LOWER DIVISION COURSE SYLLABI

LOWER DIVISION COURSE DESCRIPTIONS:

10004 Developmental Mathematics (4)
Survey of the fundamentals of mathematics. Covers real numbers, integers, equations and decimals. Hours not counted toward graduation. Prerequisite: assessment testing or permission.

10005 Introduction to College Mathematics (3)
Includes number systems, exponents, polynomials, the Cartesian coordinate system, linear and quadratic equations and inequalities. Prerequisites: appropriate placement test score or minimum C (2.0) grade in MATH 10004 and no previous mathematics courses.

Fundamental Mathematics Series
The following courses in Fundamental Mathematics are organized into 5 week long courses, offered three per semester in a time slot. A flowchart of these courses is located below to help you understand the order they should be taken. We have also included charts used by the coordinators of this course to assist in registering, to help ensure that the courses you take will follow each other in the proper order.

• Flowchart of first year courses
• FAQ's - check here for answers to some commonly asked questions
• Fundamental Math AND Modeling Algebra Course Chart for Spring 2008
• Fundamental Math AND Modeling Algebra Course Chart for Summer 2008
• Fundamental Math AND Modeling Algebra Course Chart for Fall 2008

10031 Fundamental Mathematics I (1)
Includes operations on integers, fractions, decimals and percents, properties of real numbers. Introduction to variables, first degree equations and formulas. Hours not counted toward graduation. Prerequisite: appropriate placement test score. Special
fee: $15/credit hour—subject to change.

10032 Fundamental Mathematics II (1)
Equations and inequalities in one variable, linear equations, rate of change and slope, graphing in the Cartesian coordinate system, introduction to functions. Prerequisites: appropriate placement test score or minimum C (2.0) grade in either MATH 10031 or MATH 10004. Special fee: $15/credit hour—subject to change.

10033 Fundamental Mathematics III (1)
Systems of equations, algebraic expressions, exponents and radical expressions, functions and their graphs. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10032. Special fee: $15/credit hour—subject to change.

10034 Fundamental Mathematics IV (1)
Polynomial operations and factoring, quadratic equations and functions, zeros of functions, rational expressions and functions. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10033. Special fee: $15/credit hour—subject
to change.

10035 Fundamental Mathematics V (1)
Polynomial functions, medium-level factoring techniques; solving equations and inequalities; problem solving. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10005 or 10034. Special fee: $15/credit hour—subject to change.

10036 Fundamental Mathematics VI (1)
Advanced factoring techniques; basics of exponential and logarithmic functions. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10005 or 10035. Special fee: $15/credit hour—subject to change.

10041 Elementary Probability and Statistics (3)
Descriptive statistics, probability concepts, binomial and normal distributions. Sampling, estimation, hypothesis testing. Analysis of paired data, linear models and correlation. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10005 or 10034.

11008 Explorations in Modern Mathematics (3)
Topics from various branches of mathematics are chosen to introduce students to the wide varieties of ways in which mathematics affects everyday life. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10005 or 10034. This course may be used to satisfy the Liberal Education Requirements (LER).

11009 Modeling Algebra (4)
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. Prerequisite: appropriate placement test score or a grade of C (2.0) or better in MATH 10005 or 10034; no credit for MATH 11010 or 11011. This course may be used to satisfy the Liberal Education Requirements (LER).

11010 Algebra for Calculus (3)
Study of elementary functions and graphs, including polynomial, exponential and logarithmic functions; complex numbers; binomial theorem. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10036; no credit for MATH 11011 or 12001. This course may be used to satisfy the Liberal Education Requirements (LER).

11011 College Algebra (4)
Level of difficulty between that of MATH 10005 and 12001. Includes factoring, equations, inequalities, functions, graphs, exponential and logarithmic functions. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 10005 or 10035; no credit for MATH 11010 or 12001. This course may be used to satisfy the Liberal Education Requirements (LER).

11012 Intuitive Calculus (3)
Designed to give an overview of differential and integral calculus to business and life science majors. Does not include trigonometric functions. Prerequisite: appropriate placement test score or minimum C (2.0) grade MATH 11010, 11011 or 12001. This course may be used to satisfy the Liberal Education Requirements (LER).

11022 Trigonometry (2)
Solution of triangles, trigonometric equations and identities. Prerequisite: appropriate placement test score or minimum C (2.0) grade in MATH 11011; may be taken concurrently with MATH 11010; no credit for MATH 12001.

12001 Algebra and Trigonometry (4)
Includes topics covered in MATH 11011 and 11022. Prerequisite: appropriate placement test score; no credit for MATH 11010, 11011 or 11022. This course may be used to satisfy the Liberal Education Requirements (LER).

12002 Analytic Geometry and Calculus I (5)
Concepts of limit, continuity, the derivative, and the indefinite and definite integral for functions of one real variable. Maximization, related rates. Fundamental Theorem of Calculus. Prerequisite: A grade of C (2.0) or better in MATH 12001 or in MATH 11022 and one of 11010 or 11011, or appropriate placement test score; no credit for 12011 or 12012. This course may be used to satisfy the LERs.

12003 Analytic Geometry and Calculus II (5)
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)
Introduction to differential calculus with a review of algebra and trigonometry. Includes exponents, factoring, functions, graphs, tangent lines, limits, continuity, derivatives and related rates. Prerequisite: appropriate placement test score; no credit for MATH 12002. This course may be used to satisfy the Liberal Education Requirements (LER).

12012 Calculus with Precalculus II (3)
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. Prerequisite: MATH 12011 or permission; no credit for MATH 12002. This course may be used to satisfy the Liberal Education Requirements (LER).

12021 Calculus for Life Sciences (4)
Differential and integral calculus using examples and problems in life sciences. Prerequisite: ILS major or permission.

12022 Probability and Statistics for Life Sciences (3)
Probability and statistics with applications in medical and biological sciences. Prerequisite: MATH 12021 or 12003.

14001 Basic Mathematical Concepts I (4)
Development of the real number system and its subsystems, open sentences, numeration systems, modular arithmetic and some number theory concepts. Prerequisite: appropriate placement test score or a grade of C (2.0) or better in MATH 10005 or 10034. This course may be used to satisfy the Liberal Education Requirements (LER).

14002 Basic Mathematical Concepts II (4)
Basic concepts of probability, statistics and geometry. Prerequisite: MATH 14001. This course may be used to satisfy the Liberal Education Requirements (LER).

19001 Technical Mathematics I (4)*
Introduction to geometry, algebra and trigonometry. For students in the engineering technologies. Prerequisite: three years of high school math or equivalent.

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 laboratory experience in providing explanations of mathematical concepts. May be repeated in a different area. Prerequisite: permission for one of the areas—algebra, trigonometry, mathematics education or calculus.

20095 Special Topics in Mathematics (1-5)
Various special courses will be announced in the Schedule of Classes under this course number with different section numbers. Repeated registration permitted. Prerequisite: Permission.

21001 Linear Algebra with Applications (3)
Systems of linear equations and the associated matrix operations, linear transformations, vector spaces, bases, eigenvectors. Prerequisite: MATH 11012 or 12002.

21003 Introduction to Systems Analysis and Data Communications (3)*
(Cross-listed with COMT 21003) Background in the topic of systems analysis, design, development and implementation including an overview of teleprocessing. Prerequisite: M&IS 24080.

21092 Computer Practicum (2)*
(Cross-listed with COMT 21092) Supervised work experience in a computer installation. Prerequisite: none.

22005 Analytic Geometry and Calculus III (3)
Study of functions of several variables, including partial derivatives and multiple integrals. Prerequisite: MATH 12003.

23022 Discrete Structures for Computer Science (3)
(Cross-listed with CS 23022) 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. Prerequisites: CS 10051; a grade of C (2.0) or better in MATH 12001, or in MATH 11022 and one of 11010 or 11011, or appropriate placement test score into MATH 12002; no credit for MATH 31011.

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: A grade of C (2.0) or better in MATH11010, 11011, or 12001.

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. Prerequisites: MATH 12002 and 21001 (concurrent registration in MATH 21001 allowed) and no credit for MATH 23022.

31045 Formal Logic (3)
(Cross-listed with CS 31045 and PHIL 31045) 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 22005.

34001 Fundamental Concepts of Algebra (3)
Professionalized course in algebra for prospective secondary teachers. Postulational development of number systems 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 non-parametric methods. Prerequisite: MATH 4/50011.

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. Prerequisites: MATH 21001 and 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 or permission.

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 or equivalent.

40051 Topics in Probability Theory and Stochastic Processes (3)
Topics from random walks, renewal theory, Markov processes, branching processes and birth-death processes. Brownian motion and other simple processes with applications. Prerequisite MATH 40011.

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 grading. Prerequisite: Permission.

41001 Introduction to Modern Algebra I (3)
Basic properties of groups, subgroups, factor groups. Basic properties of rings, integral domains, and homomorphisms. Prerequisites: MATH 21001 and 22005. This course may be used to satisfy the writing-intensive course graduation requirement with approval of major department.

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 or permission. This course may be used to satisfy the writing-intensive course graduation requirement with approval of major department.

41012 Finite Mathematics (3)
(Cross-listed with CS 41012) 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. Prerequisites: MATH 21001 and 22005 or permission.

41045 Metalogic (3)
(Cross-listed with CS 41045 and PHIL 41045) May be counted toward B.A. or B.S. mathematics major. See PHIL 41045 for description. Prerequisite: PHIL 31045 or permission.

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 22005 or permission. This course may be used to satisfy the writing-intensive course graduation requirement with approval of major department.

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. This course may be used to satisfy the writing-intensive course graduation requirement with approval of major department.

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. Prerequisites: MATH 21001 and 22005 or permission.

42021 Graph Theory and Combinatorics (3)
Fundamentals and applications of combinatorial mathematics. Topics include traversability, colorability, networks, inclusion and exclusion, matching and designs. Prerequisites: MATH 21001 and 22005 or permission.

42024 Numbers and Games (3)
The study of partisan and impartial combinatorial games; games as numbers; Grundy-Sprague theory. Prerequisites: MATH 21001 or permission.

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.

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 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. This course may be used to satisfy the writing intensive course graduation requirement with approval of major department.

42201 Numerical Computing I (3)
(Cross-listed with CS 42201) An introduction to numerical methods and software for solving many common scientific computing problems. Linear systems, least-square data fitting, nonlinear equations and systems, and optimization problems. Prerequisites: MATH12003, 21001, and CS23021 or permission. Special fee $3.33/cr. hr. subject to change.

42202 Numerical Computing II (3)
(Cross-listed with CS 42202) A continuation of MATH 42201. Topics include interpolation, numerical differentiation and integration, and numerical solution of ordinary differential equations. Prerequisites: MATH 32044 and CS 42201.

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 permission 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 or permission.

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: MATH 12003 or 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 or permission.

47021 History of Mathematics (3)
Survey from Babylonian and Egyptian mathematics to 20th century mathematics with emphasis on the development of algebra, geometry, calculus, and number theory. Prerequisite: 3 hours of mathematics beyond 22005 or permission.

49995 Selected Topics in Mathematics and its Applications (2-4)
(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 of instructor.

49998 Research (1-5)
Prerequisite: Permission.

GRADUATE COURSES ARE LISTED UNDER THE 'GRADUATE' TAB

*Courses offered only at Regional Campuses.