**MATH 112 ****Statistics In Daily Life**

Process of classifying and drawing conclusions form data obtained from observations, experiment, or sampling. Decision making under uncertainty with emphasis on the behavioral fields. Study of frequency distributions and their use in the decision making process. Usage of computer and prepared software make plus a graphic calculator (TI-83 or equivalent) is required.

**MATH 113** **Quantitative Reasoning**

This course provides a foundation for students to become confident and critical users of quantitative information of all kinds: numerical, graphical and verbal. Students analyze data and ideas from a wide variety of fields, such as psychology, economics, finance, sociology and political science. The course is taught in a hands-on laboratory environment where students are introduced to computer tools for data analysis and presentation. active learning and reasoning are emphasized, and technology is an intefral part of the course. Students write critiques of quantitative arguments, gather data and present arguments based on their analysis.

**MATH 145 Algebra Concepts For Middle School Teaching **

This course focuses on algebra concepts and is designed to meet the needs of elementary and middle school teachers. Some of the conceopts covered will be linear, quadratic, exponential and logarithmic functions, systems of equations and introduction to trigonomic functions. Problem solving, development of algebraic thinking and modeling simple and complex linear systems with and without technology will be emphasized. Written assignments and reflections on the learning process will be introduced as appropriate. Algebra concepts will be taught in the context of real world problems and applications. This course has been designed keeping in mind both the Illinois Content Standards for Educators in Mathematics and the National Council of Teachers of Mathematics Stadards and the content and pedagogy necessary to prepare teachers to be elementary and middle school teachers of math and science. Course is linked and integrated with the M&S Concepts Minor introductory course in biology.

**MATH 147 Statistical Concepts For Middle School Teaching **

This course has been designed keeping in mind the Illinois Content Standards for Educators in Mathematics, the National Council on Teachers of Mathematics Teaching Standards and the content within the paired interdisciplinary science course. There will be three principle components of the course: 1) descriptive statistics, 2) basic probability theory and central limit theorem, 3) applied statistics in the form of confidence intervals and hypothesis testing. Contemporary critical technologies such as data warehousing and mining, and concept modeling may be considered. This course is linked with BIO-104 Environmental Biology, and BIO-105 Environmental Biology Lab.

**MATH 149 Math For Elementary Teachers I **

This is a foundational class in mathematics for those interested in becoming elementary or middle grades teachers. Topics include place value, models for and the development of arithmetic, mental math, estimation, word problems, algorithms, factors, primes, proofs, prealgebra, fractions, ratios, rates, and percentages. Emphasis on the development of elementary mathematics from an advanced standpoint.

**MATH 150 Math For Elementary Teachers II With Problem Solving**

This is a foundational class in mathematics for those interested in becoming elementary or middle grades teachers. Topics include measurement, geometric reasoning, similarity and congruence, applications of geometry, geometric proofs, area, volume, surface area, and probability and statistics. Problem solving and mathematical thinking activities covering both number and operations and geometry content will be integrated. Emphasis is on the development of elementary mathematics from an advanced standpoint.

**MATH 151 Bridge Course In Mathematics For Elementary Teachers**

Math 151 is a course designed for students who have completed two college-level courses in math for elementary teaching at a community college. The transferred courses should focus on numbers and operations and geometry and measurement, respectively. NEIU's College of Education requires that Elementary Education majors complete at least 9 semester hours in mathematics for teachers that meet a set of common outcomes adopted by the college. This course focuses on concepts addressed by the outcomes that are not typically covered in depth by most 2-course sequences in mathematics for teaching: algebra, data analysis, statistics, probability, problem-solving and mathematical thinking. Prerequisite: MATH-151 is restricted to students majoring in Early Childhood Education, Elementary Education, Bilingual/Bicultural Education, and TCP. Enrollment by permit only.

**MATH 163 Mathematical Modeling With Elementary Functions For Business**

This course, at the College Algebra level, is designed to provide quantitative understanding and tools for business students. Students work extensively with the most important functions and equations used for applications in their fields: linear, polynomial, rational, exponential, and logarithmic.

**MATH 165 Finite Mathematics For Business And The Social Sciences**

Introduction to matrices, linear programming and probability with emphasis on mathematical models in the social, managerial and behavioral sciences and mathematics of finance.

**MATH 167 Business Calculus I **

Elements of analytic geometry, deifferential and integral calculus with application to business, economic and finance.

**MATH 173 College Algebra **

This course emphasizes the concept of a function as a unifying approach to the topics of college algebra. Families of functions studied in the course include: polynomial, rational, exponential and logarithmic functions. Other topics include conic sections, and sequences and series. Applications and problem solving skills are emphasized throughout the course.

**MATH 174 Math Enrichment Workshop For College Algebra **

Mathematics enrichment workshop for students currently enrolled in MATH 173. The workshops draw on the Peer Led Team Learning (PLTL) and Emerging Scholars Program (ESP) models, which have been nationally identified for increasing students' probability of earning higher grades in their required mathematics courses. Workshop participants will attend a workshop during the same day and time each week; collaboratively solve problems related to their standard MATH 173 course within small peer groups; receive guidance from math instructors who are specially trained to facilitate the workshops; and participate in social events with workshop peers during the semester.

**MATH 175 Trigonometry**

For students who intend to continue with Calculus I, this course uses the concept of a function as a unifying approach to the topics of trigonometry. The course studies trigonometric functions, trigonometric identities and equations, and inverse trigonometric functions. Other topics include: solving triangles, polar coordinates, complex numbers and DeMoivre's theorem; parametric equations, and vectors. Applications and problem solving skills are emphasized throughout the course.

**MATH 176 Mathematics Enrichment Workshop For Trigonometry**

Mathematics enrichment workshop for students currently enrolled in MATH 175. The workshops draw on the Peer Led Team Learning (PLTL) and Emerging Scholars Program (ESP) models, which have been nationally identified for increasing students' probability of earning higher grades in their required mathematics courses. Workshop participants will attend a workshop during the same day and time each week; collaboratively solve problems related to their standard MATH 175 course within small peer groups; receive guidance from math instructors who are specially trained to facilitate the workshops; and participate in social events with workshop peers during the semester.

**MATH 185 Precalculus**A functional approach to College Algebra and Trigonometry, for students who intend to continue with Calculus I.

**MATH 186 Mathematics Enrichment Workshop For Precalculus**

Enrichment workshop accompanying MATH-185. Students do problem solving in collaborative learning groups on material derived from and supplementing Precalculus to gain a deeper understanding of concepts and applications. Prereq.: Restricted to students taking MATH-185 concurrently.

**MATH 187 Calculus I **

Introdcution to analytic geometry, limits and derivatives, applications, integration, fundamental theorem of calculus.

**MATH 188 Mathematics Enrichment Workshop for Calculus I**

Enrichment Seminar accompanying MATH-107. Students do problem solving in collaborative learning groups on material derived from and supplementing Calculus I to gain a deeper understanding of concept and applications.

**MATH 202 Calculus II
I**ntegration techniques, applications, differential equations and series.

**MATH 203 Calculus III **

3-D analytic geometry, partial derivatives, multiple integrals and vector fields.

**MATH 204 Math Enrichment Workshop For Math 203**

Mathematics enrichment workshop for students currently enrolled in Math 203. The workshops draw on the Peer Led Team Learning (PLTL) and Emerging Scholars Program (ESP) models, which have been nationally identified for increasing students’ probability of earning higher grades in their required mathematics courses. Workshop participants will attend a workshop during the same day and time each week; collaboratively solve problems related to their standard Math 203 course within small peer groups; receive guidance from math instructors who are specially trained to facilitate the workshops; and participate in social events with workshop peers during the semester."

**MATH 251 Writing Intensive Program: Introduction To Advanced Mathematics**

A bridge course between calculus and advanced mathematics. Students study the tools and proof techniques that serve as the basis for theoretical mathematics. Mathematical structure and the development of proficiency in reading, analyzing and constructing mathematical proofs are emphasized. Topics include logic, set theory, methods of proof, combinatorics, relations, functions and cardinality.

**MATH 252 Math Enrichment Workshop For Math 251**

Mathematics enrichment workshop for students currently enrolled in Math 251. The workshops draw on the Peer Led Team Learning (PLTL) and Emerging Scholars Program (ESP) models, which have been nationally identified for increasing students’ probability of earning higher grades in their required mathematics courses. Workshop participants will attend a workshop during the same day and time each week; collaboratively solve problems related to their standard Math 251 course within small peer groups; receive guidance from math instructors who are specially trained to facilitate the workshops; and participate in social events with workshop peers during the semester.

**MATH 253 Linear Algebra I **

Matrices and systems of linear equations, analytic geometry in n-space, introduction to vector spaces, linear transformations, determinants and eigenvectors.

**MATH 262 Mathematics Enrichment Workshop For Calculus II **

Enrichment Seminar accompanying MATH-202. Students do problem solving in collaborative learning groups on material derived from and supplementing Calculus II to gain a deeper understanding of concepts and applications.

**MATH 275 Applied And Computational Statistics **

This course introduces students to the basic concepts, logic, and issues involved in statistical reasoning with wide variety of applications. It is designed to familiarize students to statistical vocabulary and concepts. Major topics include exploratory data analysis, an introduction to research methods, probability, statistical inference, and regression-based analysis of well-defined examples from biology, ecology, environmental sciences, finance, medicine, public health, psychology, and sociology. Computing will be carried out using R or SAS softwares in the course

**MATH 280 Geometry:Concepts For Middle School Teaching** (MSTQE)

This course focuses on the concepts of plane and slod geometry and trigonometry. It is designed to meet the needs of a middle school teacher in accordance with the National Council of Teachers of Mathematics Standards and the Illinois State Board of Education's Mathematics Standards. The topics include basic definitions and properties of plane and solid figures, congruence, similarity, constructions, measurements, transformations, Pythagorean Theorem, right angle trigonometry and the unit circle. Problem solving using a calculator and computer programs is emphasized throughout. Writing assignments as appropriate are also part of the course. This course is linked with PHYS-108.

**MATH 281 Number Concepts For Middle School Teaching **(MSTQE

This course has benn designed keeping in mind both the Illinois Content Standards for Educators in Mathematics and the National Council of Teachers of Mathematics Standards and the content and pedagogy necessary to prepare teachers to be elementary and middle school teachers of math and science. A wide range of topics across number theory and measurement will give the students a grasp of the depth and breadth of mathematics outside the traditional course structures. Problem solving, estimation, measurements and construction of simple theories of numbers will be treated with and without the use of technology. Writing assignments will supplant the assignments typically found in a mathematics course. This course is linked with CHEM-108.

**MATH 301 Ordinary Differential Equations I**

An introduction to Ordinary Differential Equations and applications. General first order and second order linear equations and numerical methods.

**MATH 302 Ordinary Differential Equations II **

Linear and nonlinear systems, matrix methods and applications to problems in the sciences. Existence and stability theory. Boundary value problems and Fourier series.

**MATH 303 Partial Differential Equations**

Introduction to partial differential equations and methods of finding solutions.

**MATH 304 Introduction To Numerical Analysis **

Solutions of equations of one variable, interpolation and polynomial approximation, numerical integration and methods of solutions of linear systems.

**MATH 305 Probability And Statistics**

Fundamentals and axioms; probability spaces; combinatorial probability; conditional probability; random variables; binomial, Poisson, uniform, normal, chi-square, Student's t-distribution; central limit theorem; Statistical Data Analysis: descriptive statistics, point and interval estimation, elements of hypothesis testing, small vs. large samples.

**MATH 306 Linear Programming And Extensions**

Linear programming models; geometric and algebraic foundations of the simplex algortihm; duality theory; the revised and dual algorithms; sensivity analysis; integer programming.

**MATH 307 Probability Models For Operations Research**

Basic mathematical aspects of probability models with emphasis on problem solving. Topics include Markov processes, Markov Chaings and Queuing Theory.

**MATH 309 Numerical Analysis II **

Iterative methods for linear and non-linear systems of equations, approximation of eigenvalues, initial value problems, ordinary and partial boundary value problems and approximation theory.

**MATH 312 Foundations Of Geometry **

Axiomatic systems and models of geometries. Projective and transformational geometry.

**MATH 321 History Of Mathematics**

Chronological survey of the growth of mathematical ideas, and of famous mathematicians and their contribution to the development of modern mathematics.

**MATH 322 Number Theory**

Properties of rational integers, congruences, quadratic residues and Diophantine equations.

**MATH 324 Independent Study In Mathematics**

Individual investigation into a topic of interest of the student's choice.

**MATH 326 Real Analysis**

An introduction to the methods of classical analysis as applied to the formulation of the theory of Riemann integrable functions and to the theoretical examination of the behavior of sequences and series of functions of a real variable.

**MATH 328 Complex Variables **

Introduction to the functions of a complex variable: Cauchy-reimann equations, Cauchy integral theorems and series expansions.

**MATH 331 Foundations Of Algebra I **

Introduction to abstract algebraic systems: groups, rings, fields, permulations and polynomials.

**MATH 332 Foundations Of Algebra II **

Continuation of topics adressed in MATH-331; Galois theory.

**MATH 334 Mathematical Statistics I**

Fundamentals of probability, expectations, moment generating functions, distributions: (binomial, hypergeometric, geometric, negative binomial, Poisson, uniform, gamma, exponential, chisquare, normal, beta, student-t, F), central limit theorem, convergence in distribution.

**MATH 336 Mathematical Statistics II **

Study of estimation procedures including point and interval estimation tests of hypothesis, general procedures for developing tests.

**MATH 337 Theory Of Equations **

Study of algebraic equations, existence and properties of solutions; algebraic methods of solution; numeical and algorithmic methods of solution.

**MATH 338 Advanced Calculus:Single Variable**

Advanced treatment of topics from single variable calculus, differentiation, integraton, power series, improper integrals, gamma functions and Laplace transforms with emphasis on both theory and applications.

**MATH 339 Advanced Calculus:Multi-Variable **

Advanced treatment of topics from the calculus of several variables using topology and linear algebra as tools. Partial differentiation, multiple integration, Green's theorem are treated both theoretically and with a view towards applications.

**MATH 340 Computing For Mathematicians**

Fundamentals of compouter programming, experimentation, and simulation in mathematics with Maple and Fortran programming language. Introduction to documentation, electronic communication and problem solving in mathematical sciences. No prior computer skills required.

**MATH 343 Linear Algebra II **

A continuation of MATH-243 with emphasis on computational mehtods and application, LU, QR and SVD Factorizations.

**MATH 365 Statistical Computer And Data Analysis Packages **

Study of topics from current statistical packages such as SAS, SPSS, BMDP and MINITAB.

**MATH 370 Mathematical Modeling In The Natural Sciences **

This course focuses on the formulation, analysis, and interpretation of mathematical models describing certain phenomena in the natural sciences. Topics include: difference equations, systems of difference equations, nonlinear difference equations, continuous models, phase planes – stability analysis, and limit cycles.

**MATH 374 Modeling And Simulations Of Complex Systems **

This course covers basic mathematical and statistical methods for analyzing computational spatial models in various applications, focusing on individual attributes (social influence or contagion) and network structure of groups. The course will incorporate simple graph theoretical approaches and construction and analysis of social network-based models (NBM) and agent-based models (ABM) with complex systems applications from epidemiology, finance/business, medicine, psychology, and social sciences. The NBM involves the characterization of the structures of social networks or subsets of these networks to understand their influence on behaviors and outcomes. The ABM involves the use of stochastic computer simulations of simulated individuals, in simulated space, over simulated time to understand how macro-level distribution patterns of outcomes may emerge from explicitly programmed, micro-level behaviors, social interactions, and movement of these individuals in their environments. Students will interpret published research and produce a research proposal by the end of the semester.

MATH 380 Calculus Concepts For Middle School Teachers Course is designed keeping in mind the Illinois Content Standards for Educators in Mathematics, the National Council of Teachers of Mathematics Teaching Standards and the Understanding that many of the students are preparing to be middle school mathematics teachers. Course emphasis is on conceptual knowledge, content specific knowledge and pedagogical knowledge. Course will focus on real applications including applications to study of ecology and change and on process no procedures. Topics are consistent with a standard calculus course and include: analytical geometry, limts and derivatives, diffrential equations, polynomials, applications, integration, series, fundamental theorem of calculus. This course is integrated with NEIUBIO-299.

MATH 381 Concepts In Discrete Mathematics For Middle School Teachers "Designed especially for middle school teachers, this course provides a foundational experience in discrete mathematics through an emphasis on topics in graph theory. Students will learn about mathematics as an active process of making conjectures, testing ideas, and proving conclusions. Special emphasis is given to mathematical communication, problem-solving, and applications to the sciences. Topics include: the Four Color Theorem, trees, digraphs, bipartite graphs, planar graphs, Platonic solids, Euler and Hamilton circuits, the P+NP Problem, algorithms and combinatorial explosion. Students will first learn the mathematics and then explore how it connects to the middle school curriculum.

MATH 406 Linear Programming: Theory And Practice Optimization models; theoretical foundations of simplex algorithms and duality; revised and dual algorithms; sensivity and analysis; additional topics from extended LP interger programming, networks, recent trends.

MATH 408 Mathematics Structures For Elementary School Teachers I Mathematics topics and techniques that are relevant to advanced mathematics learning and the teaching of mathematics in the schools: Elementary logic, elementary sets, binary operations, introduction to algebraic structures, number systems, geometry and elements of graph theory.

MATH 409 Mathematical Functions For Elementary School Teachers I For elementary school teachers. The function concept; polynomial functions; solution of linear and quadratic equations; simultaneous equations; the binomial theorem; circular functions; solution of triangles; trigonometric identities and equations; exponential and logarithmic functions; rectangular and polar coordinate systems; the conic sections. Graphics calculator required.

MATH 410 Modern Analysis For The Elementary School Teacher Limits and continuity, derivatives, applications, integral calculus, applications.

MATH 421 Modern Geometry Classification of geometrical systems; introduction to Euclidean and non-Euclidean geometries, projective geometry; finite geometries.

MATH 430 Discrete Mathematical Structures Provides a working knowldge of mathematical logic, sets, relations, functions, graphs, and counting techniques.

MATH 435 Mathematics Structure II The real number system, mathematical systems, inductive and deductive methods, permutations and combinations.

MATH 436 Modern Algebra

MATH 439 Computers In Education Investigation into the use of computers for CAI, statistical packages and solutions of mathematical problems. Students learn to write programs in Basic.

MATH 441 Multivariate Statistical Analysis The essential methods of the multivariate statistical analysis; Hotteling's T, discriminant function, principal components, factor analysis, canonical correlations and cluster analysis with emphasis on application and real data analysis.

MATH 442 Applied Regression Analysis Methodology of regression analysis with attention to model building, evaluating fit, and examining reliability of the model; regression and general least squares theory, estimation of regression coefficients, polynomial regression, step-wise regression, residual analysis, choice of transformation for variable and forecasting; with applications and real data analysis.

MATH 443 Experimental Design One-way and two-way analysis of variance, fixed and random effects models, multiple comparisons, completely randomized and randomized block designs.

MATH 457 Recent Trends In Mathematics Extended applications of mathematical thinking, operations research, mathematical models, information theory, theory of games, and linear programming.

MATH 465 Advanced Topics In Numerical Analysis Possible topics include numerical linear algebra, iteration methods and convex programming, numerical methods for ordinary and partial differential equations, functional approximation and data analysis, digital spectral analysis, design and analysis of mathematical software, and mathematical methods in computer graphics. Consult the Schedule of Classes for specific topics.

MATH 466 Galois Theory: Historical And Modern Classical and modern Galois theory. Cardano's formulas, symmetric polynomials, permutation groups, field extensions, field automorphisms, the fundamental theorem of Galois theory.

MATH 471 Introduction To Stochastic Models Markov Chains: the Poisson process; continuous time Markov processes; Renewal Theory; Queuing Theory.

MATH 472 Simulation Modeling And Analysis Design and analysis of computer simulations of complex systems. Network, discrete event and continuous models are treated in a unifying setting. Computer model of a variety of systems are implemented and analyzed using a general purpose simulation language.

MATH 473D Advanced Topics In Operations Research: Decision Theory

MATH 474 Mathematical Modeling Formulation, analysis and interpretation of mathematical models describing phenomena from the natural and social sciences. Topics may include: model construction, explicative versus predictive models, model fitting, optimization, empirical models, simulation models, dynamical models, dimensional analysis and other related topics. A term project (team or individual) will be required.

MATH 475 Advanced Topics In Operations Research: Mathematical Programming This course offers an overview of deterministic optimization models and methods including linear programming methods, multi-objective optimization, methods of discrete optimization, and nonlinear programming methods.

MATH 475F Advanced Topics In Operations Research: Topics In Quantitative Finance This course offers an overview of deterministic optimization models and methods including linear programming methods, multi-objective optimization, methods of discrete optimization, and nonlinear programming methods.

MATH 476 Special Topics: Chaos And Dynamical Systems The aim of this course is to introduce mathematicians to current research in dynamical systems and chaos theory and their applications. Topics to be covered include chaos, elementary bifurcations, Sarkovskii's Theorem, Schwarzian derivative, symbolic dynamics, chaotic behavior, and homoclinic phenomena. In this course we will also discuss higher dimensional dynamics, including special examples like the horseshoe and strange attractors. We will discuss the stable manifold theorem in its most elementary setting and also such higher dimensional bifurcations such as the Hopf bifurcation. The course will conclude with special topics in discrete dynamics such as complex dynamics or the Lorenz attractor.

MATH 491 Independent Study In Mathematics Individual investigation into a topic of interest of the student's choice.

MATH 492 Independent Study In Mathematics (See MATH-491 for descriptions.)

MATH 493 Independent Study In Mathematics (See MATH-491 for descriptions.)

MATH 494 Thesis Seminar - Mathematics Students conduct research and write a thesis to fulfill requirements for the Master of Science degree.

MATH 495 Project In Mathematics Students prepare a project involving both the theory and computational tools learned in their concetration. Students present both written and oral reports to the deparment.