# Mathematics Courses

**MATH009 Computational Skills**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

An arithmetic or pre-algebra course that is intended for students who need to improve their basic computational skills. It contains work with whole numbers, fractions, decimals, ratios and proportions, percents, descriptive statistics, geometry and measures, signed numbers, and solving simple equations and problems.

Prerequisite: None

Corequisite: None

**MATH100**** Essentials of Algebra**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A one-term introductory algebra course intended for students who have a firm background in arithmetic but need to improve their algebra skills in preparation for general education mathematics courses. It covers real and rational numbers and algebraic expressions, solving equations and inequalities, polynomials, graphs, systems of equations, radicals, and quadratic equations.

Prerequisite: ( MATH009 )

Corequisite: None

**MATH101**** Topics in Math**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A presentation of topics from number theory, topology, set theory, algebra, and analysis. Each of the topics included in the course is subjected to careful mathematical analysis.

Prerequisite: ( MATH009 )

Corequisite: None

**MATH102**** Number Systems**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A presentation of the mathematical ideas and skills for teachers of grades K-8. Topics included in Number Systems are problem solving, sets and relations, systems of numeration, number systems, and consumer mathematics.

Prerequisite: ( MATH100 ) OR ( MATH112 ) OR ( MATH113 ) OR ( MATH141 ) OR ( MATH215 )

Corequisite: None

**MATH107**** Basic Statistics 1**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A presentation of both basic concepts and computational methods involved in the analysis of sample distributions, with consideration given to probability theory; and a thorough introduction to statistical inference.

Prerequisite: ( MATH100 ) OR ( MATH112 ) OR ( MATH113 ) OR ( MATH141 )

Corequisite: None

**MATH108**** Basic Statistics 2**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

The major topics are regression and analysis of variance. Multiple regression, along with both one and two-way analysis of variance, are studies.

Prerequisite: ( MATH107 )

Corequisite: None

**MATH110**** Consumer Math**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

A practical course designed to provide the student with information and computational skills necessary for money management. Topics include: interest, taxes, buying, credit, banking, insurance, annuities, international business, investments, and financial planning.

Prerequisite: ( MATH009 )

Corequisite: None

**MATH112**** Intermediate Algebra**[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

Assists students in acquiring a thorough knowledge and proficiency in college algebra. The contents of the course includes an introduction to sets of real numbers and properties, polynomial and rational expressions, rational exponents and radicals, equations and inequalities, complex numbers, and the Cartesian coordinate system. It also introduces the concept of functions and their graphs. The presentation of topics is balanced between theory and application.

Prerequisite: ( MATH100 )

Corequisite: None

**MATH113 Precalculus**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

An introduction to concept of functions and study of several elementary functions. The contents of the course include properties and graphs of polynomial, exponential, logarithmic, and trigonometric functions. This material is treated in the modern spirit with emphasis placed on both the development of pertinent concepts as well as the acquisition of essential techniques. The presentation of the topics is balanced between theory and application.

Prerequisite: ( MATH112 )

Corequisite: None

**MATH115**** Statistics and Geometry**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A presentation (along with MATH102 Number Systems) of the mathematical ideas and skills for teachers of grades K-6. Topics included in Statistics and Geometry are probability, statistics, measurement, and two and three-dimensional geometry.

Prerequisite: ( MATH100 )

Corequisite: None

**MATH119**** First Year Student Seminar**

[Minimum Semester Hours: 1 sh; Maximum Semester Hours: 1 sh]

Designed to embed education program requirements into a required course and to support student achievement of Education Program requirements. This course addresses topics taught in freshman seminars. Restricted to first-year secondary education mathematics majors or B.A. mathematics majors.

Prerequisite: None

Corequisite: None

**MATH125**** Introduction to Secondary Mathematics**

[Minimum Semester Hours: 1 sh; Maximum Semester Hours: 1 sh]

An introduction to the history of education and mathematics education, leading up to an examination of the various standards used in teaching mathematics in the 21st century. The organizational structure of secondary schools and the diverse needs of grades 7-12 students are embedded in the previously mentioned topics.

Prerequisite: None

Corequisite: None

**MATH135**** Applied Algebra and Trigonometry**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

Concepts of functions and their graphs are defined and basic combinations of functions are introduced. Properties and graphs of linear, quadratic, and periodic functions are discussed. Trigonometric functions, identities and equations are discussed and graphs of various combinations of trigonometric functions are explored. Some properties such as areas and volumes of geometrical figures are discussed and vectors are introduced. Regression line and estimation of parameters are discussed. Applications in Physical Sciences are also explored.

Prerequisite: ( MATH112 )

Corequisite: None

**MATH141**** Calculus 1**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A review of algebraic functions, trigonometric functions, and elementary analytic geometry. Limits of functions and continuity are introduced. The derivative of a function is defined and properties of the derivative are applied to a variety of problems. The integral is defined and the Fundamental Theorem of Calculus is introduced and used in the evaluation of integrals.

Prerequisite: ( MATH113 )

Corequisite: None

**MATH142**** Calculus 2**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

A presentation of the calculus of transcendental functions. Integration is studied in depth, specifically techniques of integration and applications, as well as improper integrals. Conic sections and indeterminate forms are studied.

Prerequisite: ( MATH141 )

Corequisite: None

**MATH180**** Mathematics for Management**[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

An introduction to the basic techniques for solving systems of linear equations and their extension to the simplex method for solving linear programming problems. Conditional probability is re-examined and extended to Markov Processes.

Prerequisite: ( MATH107 AND MATH112 )

Corequisite: None

**MATH200 Secondary Mathematics Methods 1**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

Provides the first in a two-course sequence of methods of teaching mathematics in
grades 7-12. This course includes field experiences and practice teaching. The concentration
in this course is on the nature of mathematics, psychology of learning mathematics,
teaching of mathematics, history of mathematics education, national and state standards,
lesson planning, mathematics-oriented technology, and diversity issues. In addition
to these, as the specific topics arise, the course helps students understand the mathematics
concepts they will be teaching.

Prerequisite: ( EDTF101 AND MATH141 AND PSYC103 AND SPEC204 )

Corequisite: None

**MATH205**** Foundations of Mathematics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

Provides the foundation that is necessary for students to make the transition to advanced mathematics. Basic topics of Mathematical Logic with deductive reasoning as applied to mathematical proofs are studied in detail. Mathematical Induction, Set Theory and Theory of Relations and Functions are studied with appropriate proofs.

Prerequisite: ( MATH141 )

Corequisite: None

**MATH211**** Linear Methods**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

Vector spaces, matrices, linear transformations, and systems of linear equations are defined and the properties of these structures are developed through examples and, to a lesser degree, proof-theoretic techniques. Inner product spaces, eigenvalues, and eigenvectors are also explored. Euclidean vector spaces are emphasized throughout.

Prerequisite: ( MATH141 )

Corequisite: None

**MATH218**** Technology in Secondary Mathematics**

[Minimum Semester Hours: 1 sh; Maximum Semester Hours: 1 sh]

An introduction to the use of technology in teaching mathematics. The history of using technology in teaching mathematics and current trends are examined. Topics include, but are not limited to, calculators (standard, scientific, and graphing), handheld computers, laptops, Computer Assisted Instruction, Computer Algebra Systems, virtual manipulatives, dynamic geometry software, statistical software, and interactive whiteboards.

Prerequisite: None

Corequisite: None

**MATH225**** History of Mathematics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A development of the history of mathematics, interwoven with biographical sketches and outstanding achievements. Begins with the great civilizations of antiquity and progresses through the twentieth century. Addresses contributions from underrepresented groups in a variety of ways. Students study how contributions from culturally diverse populations have significantly aided the development of the field of mathematics, and how mathematics has changed the culture of diverse populations.

Prerequisite: ( MATH141 )

Corequisite: None

**MATH243**** Calculus 3**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A study of multivariate calculus and its applications, along with three-dimensional analytic geometry. A study of sequences and series, culminating with power series representation for functions, is presented. Polar equations and their graphs are studied.

Prerequisite: ( MATH142 )

Corequisite: None

**MATH244**** Calculus 4**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

Concludes the undergraduate study of calculus with a detailed treatment of vector analysis, culminating in the three integral theorems of vector analysis: the divergence theorem, Green's theorem, and Stokes' theorem.

Prerequisite: ( MATH243 )

Corequisite: None

**MATH301**** Differential Equations**[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

An introduction to techniques of solving first and second order ordinary differential equations along with their applications including initial value and boundary value problems. Methods of solution for first order differential equations are developed. Basic theory of linear differential equations is presented with special emphasis on second order differential equations. Laplace transforms and the major theorems are studied and utilized in problem solving. Systems of linear differential equations and series solutions are introduced.

Prerequisite: ( MATH243 )

Corequisite: None

**MATH302 Number Theory**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

The study of the divisibility properties of the integers. Topics include the congruence relations, arithmetic functions, Gauss' Law of Quadratic Reciprocity, and Diophantine equations as well as applications such as cryptography.

Prerequisite: ( MATH205 )

Corequisite: None

**MATH307**** Foundations of Geometry**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

An axiomatic study of various geometries including finite geometry, absolute (neutral) geometry, Euclidean geometry, Lobachevskian geometry, and Riemannian geometry. Historical and cultural frameworks for these geometries are provided.

Prerequisite: ( MATH205 )

Corequisite: None

**MATH310**** Modern Algebra 1**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

An investigation into algebraic structures including groups, rings, and fields. Special emphasis is placed on the concept of isomorphism and the application of these concepts to the algebra of the secondary education classroom.

Prerequisite: ( MATH205 )

Corequisite: None

**MATH311**** Elements of Linear Algebra**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

An investigation of systems of linear equations, matrices, determinant function, vector spaces, inner product spaces, linear transformations, eigenvalues, and eigenvectors. It develops properties of these structures through proof-theoretic techniques. It explores applications to areas such as geometry, economics, physical sciences, and social sciences.

Prerequisite: ( MATH205 )

Corequisite: None

**MATH312**** Probability & Statistics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

The mathematical treatment of probability is covered. An introduction to probability theory is done using an axiomatic approach. A discussion of the frequently used probability distributions and counting techniques are covered. The properties and interrelations of some important probability distributions are studies using mathematical ideas of calculus and set theory. Statistical theory and methods are introduced and topics such as estimation and hypothesis testing are studied.

Prerequisite: ( MATH243 )

Corequisite: None

**MATH313**** Mathematical Statistics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

Theoretical treatment of statistical topics such as probability distribution functions--binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, gamma, exponential, chi-square, F, beta, Pareto, lognormal, Weibull, t, and normal--moment generating functions, sampling distribution, order statistics, point and interval estimation, maximum likelihood estimation, hypothesis testing, Neyman-Pearson Lemma, and decision theory.

Prerequisite: ( MATH312 )

Corequisite: None

**MATH316**** Secondary Mathematics Methods 2**

[Minimum Semester Hours: 4 sh; Maximum Semester Hours: 4sh ]

Provides the second in a two-course sequence of methods of teaching mathematics in grades 7-12. This course includes field experiences and practice teaching. The concentration in this course is on instructional strategies for specific content, the problems of practice, curriculum, unit and lesson planning, assessment, reading and writing strategies in mathematics, technology, diversity issues, adaptations for special needs, and professionalism. In addition to these, as the specific topics arise, the course helps students more deeply understand the mathematics concepts they will be teaching.

Prerequisite: None

Corequisite: None

**MATH320**** Linear Programming**[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

A presentation of the theory of linear programming as well as applications in which linear programming finds its utility, including operations research/management science, game theory, and graph theory.

Prerequisite: ( MATH211 ) OR (MATH311)

Corequisite: None

**MATH327 Pedagogical Content Knowledge in Secondary Mathematics 1**

[Minimum Semester Hours: 1 sh; Maximum Semester Hours: 1 sh]

A partial review of the mathematics taught in secondary schools, examining it from
an advanced standpoint, and connecting it to the mathematics studied at the university.

Prerequisite: None

Corequisite: None

**MATH328**** Mathematical Science Seminar**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

This seminar has featured such topics as the study of the history of mathematics, the impact and potential effects of computers upon society, and the study of mathematics as it occurs with society in the forms of puzzles, games, and other types of recreation.

Prerequisite: None

Corequisite: None

**MATH350**** Numerical Methods**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

An introduction to numerical methods in the solution of non-linear equations, systems of linear equations, numerical integration, and numerical differentiation. The course will entail both mathematical rigor and computational aspects of some widely used numerical methods. Commercially-produced programs from the MATLAB library will be used.

Prerequisite: (MATH243)

Corequisite: None

**MATH401**** Real Analysis**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A mathematically rigorous introduction to analysis of a real valued function of a single real variable. Mathematical logic, set theory, relevant topological and algebraic properties together with proof techniques are heavily utilized throughout the course. Convergence, continuity, differentiation, integration and their interconnections are studied with mathematical integrity.

Prerequisite: ( MATH205 AND MATH243 )

Corequisite: None

**MATH402**** Real Analysis 2**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A continuation of MATH401 - Real Analysis I. Convergence questions regarding sequences and series of real functions are investigated. The Lebesque integral is defined and its existence and properties are investigated. Several basis theorems about Fourier series are explained and proved. Real-valued functions of several real variables are defined and several related theorems are deduced.

Prerequisite: ( MATH401 )

Corequisite: None

**MATH403**** Biomathematics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

An introduction to the area of mathematical biology, and the aim is to develop mathematical representation, treatment and modeling of biological processes, using applied mathematical techniques and tools. An emphasis shall be placed upon methods from difference and differential equations. Topics include the study of single species population dynamics, population dynamics or interacting species, models for the spread of infectious diseases, population genetics and evolution, molecular and cellular biology models, and tumor models.

Prerequisite: ( MATH301 )

Corequisite: None

**MATH404**** Applied Mathematics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

The investigation of the concept of mathematical model as it is used in Applied Mathematics. Different models are presented as a means of providing solutions to practical problems.

Prerequisite: ( MATH301 )

Corequisite: None

**MATH405**** Complex Analysis**[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3sh ]

Prerequisite: ( MATH243 )

Corequisite: None

**MATH410 Intro to Topology**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

The course is an introduction to the elements of set theory and topology. Topics could
include introductory set theory, a detailed study of the real line, topological spaces,
metric spaces, functions and continuity, compactness, connectedness, completeness,
product spaces, function spaces.

Prerequisite: ( MATH401 )

Corequisite: None

**MATH412**** Actuarial Mathematics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

A formulation, analysis and interpretation of mathematical models in financial mathematics and interest theory, and how these concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for use in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. Financial instruments, including derivatives, and the concept of no-arbitrage are covered. This course covers materials for the second actuarial exam, Exam 2- Financial Mathematics (FM).

Prerequisite: ( MATH243 )

Corequisite: None

**MATH415**** Student Teaching and Practicum Secondary 1: Mathematics**

[Minimum Semester Hours: 7 sh; Maximum Semester Hours: 7 sh]

Student teaching provides the capstone experience for preservice teachers. Two student teaching experiences are provided at two levels (appropriate to certification areas and grade level ranges). Supervised practice in classrooms with certified teachers introduces the student to all aspects of the teaching day. University professors supervise the student teachers and conduct weekly practicum sessions.

Prerequisite: None

Corequisite: None

**MATH416**** Student Teaching and Practicum Secondary 2: Mathematics**

[Minimum Semester Hours: 7 sh; Maximum Semester Hours: 7 sh]

Student teaching provides the capstone experience for preservice teachers. Two student teaching experiences are provided at two levels (appropriate to certification areas and grade level ranges). Supervised practice in classrooms with certified teachers introduces the student to all aspects of the teaching day. University professors supervise the student teachers and conduct weekly practicum sessions.

Prerequisite: None

Corequisite: None

**MATH422**** Applied Statistics**

[Minimum Semester Hours: 3 sh; Maximum Semester Hours: 3 sh]

Comprehensive treatment of regression analysis. Topics include simple and multiple linear regression, least square estimates, ANOVA, ANCOVA, F-test, R-square, selections of the "best subset" of predictor variables, contingency tables and basic categorical data analysis methods, checking model assumptions and Logistic regression. Computer packages, MINITAB or SPSS, will be used throughout the course. Emphasis will be given to conceptual understanding, data analysis, and applications.

Prerequisite: ( MATH312 )

Corequisite: None

**MATH427**** Pedagogical Content Knowledge in Secondary Mathematics 2**

[Minimum Semester Hours: 2 sh; Maximum Semester Hours: 2 sh]

A continuation of MATH327 where the mathematics taught in secondary schools is examined from an advanced standpoint and connected to the mathematics studied at the university. The course includes field experience in secondary schools.

Prerequisite: None

Corequisite: None

**MATH493**** Student Teaching and Professional Practicum 1**

[Minimum Semester Hours: 6 sh; Maximum Semester Hours: 6sh ]

The first of two capstone experiences (one at each level appropriate to certification areas and grade level ranges) for pre-service teachers through a student teaching experience required for certification in secondary mathematics. Supervised practice in classrooms with certified teachers and regular practicum sessions, according to prescribed guidelines, introduce the student to the range and scope of a professional educator's responsibilities.

Prerequisite: None

Corequisite: None

**MATH494**** Student Teaching and Professional Practicum 2**[Minimum Semester Hours: 6 sh; Maximum Semester Hours: 6sh ]

The second of two capstone experiences (one at each level appropriate to certification areas and grade level ranges) for pre-service teachers through a student teaching experience required for certification in secondary mathematics. Supervised practice in classrooms with certified teachers and regular practicum sessions, according to prescribed guidelines, introduce the student to the range and scope of a professional educator's responsibilities.

Prerequisite: None

Corequisite: None

**MATH605 Probability (3.0 sh)**

The mathematical treatment of probability is covered. Introductory topics included: counting principles, subadditivity formulas, independence and conditional probability. There is also a thorough treatment of discrete and continuous random variable, both univariate and multivariate, including traditionally discussed examples (including Binomial, Negative Binomial, Poisson, Normal, Gamma), properties of expected value, statistical independence, moment generating functions and transformations of random variables. This course covers materials for the actuarial exam P (Probability).

Prerequisite: None

Corequisite: None

**MATH610 Introduction to Financial Mathematics (3.0 sh)**

Formulation, analysis and interpretation of mathematical models in financial mathematics and interest theory, with applications to present and accumulated values for various streams of cash flows are covered. Topics in the theory of interest include the time value of money, annuities, loans, bonds, general cash flows and portfolios and immunization. Financial instruments, including derivatives, options, forwards, futures, swaps and the concept of no-arbitrage are covered. This course covers materials for the actuarial exam FM (Financial Mathematics).

Prerequisite: None

Corequisite: None

**MATH615 Actuarial Models and Life Data Analysis 3.0 sh**

A discussion of the traditional actuarial models and theory of life contingencies with modern computational techniques. Emphasis is placed on the practical context for the survival models and valuation methods necessary to foster general business awareness in the life insurance context and to develop the mathematical tools necessary for risk management in this context. This course covers materials for the actuarial exam MLC (Models for Life Contingencies).

Prerequisites: MATH605 and MATH610

**MATH620 Mathematical Statistics 3.0 sh**

A rigorous mathematical foundation of inferential statistics. The sampling distribution for the mean, proportion, difference between two means or proportions, prediction intervals and tolerance limits, variance and ratio of two variances. One-sided and two-sided confidence intervals will be covered, and hypothesis testing of population claims will be studied. Chi-square goodness-of-fit tests, the Neyman Pearson Lemma and decision theory will be discussed, as well as an introduction to simple linear regression.

Prerequisites: MATH605

**MATH625 Regression Analysis and Sta****tistical Models 3.0 sh**

An introduction to linear regression is covered. Simple linear regression with least squares estimates and general regression models with hypotheses testing and confidence intervals for regression parameters are studied. Multiple linear regression with least squares estimation, matrix approach, hypotheses testing, and ANOVA are covered. Testing of models, data analysis and appropriateness of models are covered. Use of dummy variables and selections of the "best subset" of the predictor variable are discussed, along with logistic regression.

Prerequisites: MATH620

**MATH630 Time Series and Forecasting 3.0 sh**

An introduction to time series and forecasting. Topics include an introduction to prediction using time-series regression methods with seasonal and non-seasonal data. The use of data observed and collected over a series of time is used to model and forecast using univariate, autoregressive, and moving average models. Smoothing methods for forecasting are also covered.

Prerequisites: MATH625