**MATH-112. Statistics In Daily Life. 3 Hours.**

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.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-113. Quantitative Reasoning. 3 Hours.**

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.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-141. College Mathematics I. 3 Hours.**

The purpose of this course is to introduce the students to several of the mathematical tools that are used in all areas of mathematics including subjects that are strongly mathematics driven; these tool facilitate (1) problem-solving in mathematics and (2) mathematical communication and connection with other branches and other disciplines. Graphing calculator will be required and used to facilitate better understanding of some mathematical models, algorithms and applications. Other topics include expressions, mathematical functions, equations, inequalities and complex numbers.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-143. College Mathematics II. 3 Hours.**

The purpose of this course is to introduce the new teachers to the structure of Mathematics which include: mathematical reasoning; mathematical communication and connection with other branches and other disciplines; and problem-solving. Topics: number theory, combinatorics, geometry, probability and statistics, mathematics of finance.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-145. Algebra Concepts For Middle School Teaching. 4 Hours.**

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.**Prerequisite: ** MATH-141 minimum grade of C or MATH-108 minimum grade of C or NEIU Math Placement Result 30 or ACT Math 22 or ACT Math 23 or ACT Math 24.**Corequisite: ** BIO-199.

**MATH-147. Statistical Concepts For Middle School Teaching. 4 Hours.**

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.**Prerequisite: ** MATH-141 minimum grade of C or MATH-108 minimum grade of C or NEIU Math Placement Result 30 or ACT Math 22 or ACT Math 23 or ACT Math 24 or Accuplacer College Level Math-020 or Accuplacer College Level Math-021 or Accuplacer College Level Math-022 or Accuplacer College Level Math-023 or Accuplacer College Level Math-024 or Accuplacer College Level Math-025 or Accuplacer College Level Math-026 or Accuplacer College Level Math-027 or Accuplacer College Level Math-028 or Accuplacer College Level Math-029 or Accuplacer College Level Math-030.**Corequisites: ** BIO-104, BIO-105.

**MATH-149. Math For Elementary Teachers I. 4 Hours.**

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.**Prerequisite: ** MATH-092 minimum grade of C.

**MATH-150. Math For Elementary Teachers II With Problem Solving. 5 Hours.**

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.**Prerequisite: ** MATH-149 minimum grade of C.

**MATH-151. Bridge Course In Mathematics For Elementary Teachers. 3 Hours.**

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. 3 Hours.**

This course, at the College Alebra 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.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-164. Modeling With Elementary Functions For Business Seminar. 1 Hour.**

Enrichment Seminar accompanying MATH-163. Students engage in problem solving in collaborative learning groups on material derived from and complementing Mathematical Modeling with elementary functions in Business to gain a deeper understanding of concepts and application.**Corequisite: ** MATH-163.

**MATH-165. Finite Mathematics For Business And The Social Sciences. 3 Hours.**

Introduction to matrices, linear programming and probability with emphasis on mathematical models in the social, managerial and behavioral sciences and mathematics of finance.**Prerequisite: ** (MATH-163 - 499 or MATH-163A - 499Z or NEIU Math Placement Result 35 - 40 or ACT Math 25 - 36 or Accuplacer College Level Math-031 - 120).

**MATH-167. Business Calculus I. 4 Hours.**

Elements of analytic geometry, deifferential and integral calculus with application to business, economic and finance.**Prerequisite: ** (MATH-163 - 499 or MATH-163A - 499Z or NEIU Math Placement Result 35 - 40 or ACT Math 25 - 36 or Accuplacer College Level Math-031 - 120).

**MATH-173. College Algebra. 4 Hours.**

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.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-174. Math Enrichment Workshop For College Algebra. 1 Hour.**

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.**Corequisite: ** MATH-173.

**MATH-175. Trigonometry. 3 Hours.**

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.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-176. Mathematics Enrichment Workshop For Trigonometry. 1 Hour.**

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.**Corequisite: ** MATH-175.

**MATH-177. Elementary Functions In The Sciences/Math. 3 Hours.**

This is an application inspired college algebra course which covers linear, quadratic, general polynomial, exponential and logarithmic functions using applications from science and mathematics. Arithmetic and geometric sequences are introduced as difference equations to motivate the study of quantities that change over time. Curve fitting is used to interpret data. A graphing calculator is required.**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-178. Elementary Functions In The Sciences/Math Seminar. 1 Hour.**

Enrichment Seminar accompanying MATH-177. Students do problem solving in collaborative learning groups on material derived from and complementing Mathematical Modeling with Elementary Functions in the Sciences and Mathematics to gain a deeper understanding of concepts and applications. The contend of the seminar is closely aligned with the contend of MATH-177.**Corequisite: ** MATH-177.

**MATH-185. Precalculus. 4 Hours.**

A functional approach to College Algebra and Trigonometry, for students who intend to continue with Calculus I.**Prerequisite: ** (MATH-173 - 499 or MATH-173A - 499Z or NEIU Math Placement Result 35 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-031 - 120).

**MATH-186. Mathematics Enrichment Workshop For Precalculus. 1 Hour.**

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.**Corequisite: ** MATH-185.

**MATH-187. Calculus I. 4 Hours.**

Introdcution to analytic geometry, limits and derivatives, applications, integration, fundamental theorem of calculus.**Prerequisites: ** (MATH-185 - 499 or MATH-185A - 499Z or NEIU Math Placement Result 40 - 45 or ACT Math 28 - 36 or Accuplacer College Level Math-061 - 120 or (MATH-173 and MATH-175)).

**MATH-188. Mathematics Enrichment Workshop for Calculus I. 1 Hour.**

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.**Corequisite: ** MATH-187.

**MATH-199S. Topics In Probability And Statistics For Middle School Teaching. 4 Hours.**

**MATH-202. Calculus II. 4 Hours.**

Integration techniques, applications, differential equations and series.**Prerequisite: ** (MATH-187 or MATH-107 or NEIU Math Placement Result 40 - 45 or Accuplacer College Level Math-061 - 120).

**MATH-203. Calculus III. 4 Hours.**

3-D analytic geometry, partial derivatives, multiple integrals and vector fields.**Prerequisite: ** MATH-202 minimum grade of C.

**MATH-204. Math Enrichment Workshop For Math 203. 1 Hour.**

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.**Corequisite: ** MATH-203.

**MATH-251. Writing Intensive Program: Introduction To Advanced Mathematics. 5 Hours.**

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.**Prerequisites: ** (MATH-187 minimum grade of C or MATH-107 minimum grade of C or NEIU Math Placement Result 40) and ENGL-101 minimum grade of C.

**MATH-252. Math Enrichment Workshop For Math 251. 1 Hour.**

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.**Corequisite: ** MATH-251.

**MATH-253. Linear Algebra I. 3 Hours.**

Matrices and systems of linear equations, analytic geometry in n-space, introduction to vector spaces, linear transformations, determinants and eigenvectors.**Prerequisites: ** (MATH-187 minimum grade of C or MATH-107 minimum grade of C or NEIU Math Placement Result 40) and MATH-251 minimum grade of C.

**MATH-262. Mathematics Enrichment Workshop For Calculus II. 1 Hour.**

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.**Corequisite: ** MATH-202.

**MATH-273. Statistics With Applications. 4 Hours.**

**Prerequisite: ** (MATH-092 - 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120).

**MATH-275. Applied And Computational Statistics. 4 Hours.**

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.**Prerequisite: ** MATH-173 minimum grade of C.

**MATH-280. Geometry:Concepts For Middle School Teaching. 4 Hours.**

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.**Prerequisite: ** MATH-141 minimum grade of C or MATH-108 minimum grade of C or NEIU Math Placement Result 30 or ACT Math 22 or ACT Math 23 or ACT Math 24 or Accuplacer College Level Math-020 or Accuplacer College Level Math-021 or Accuplacer College Level Math-022 or Accuplacer College Level Math-023 or Accuplacer College Level Math-024 or Accuplacer College Level Math-025 or Accuplacer College Level Math-026 or Accuplacer College Level Math-027 or Accuplacer College Level Math-028 or Accuplacer College Level Math-029 or Accuplacer College Level Math-030.**Corequisite: ** PHYS-108.

**MATH-281. Number Concepts For Middle School Teaching. 4 Hours.**

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.**Prerequisite: ** MATH-141 minimum grade of C or MATH-108 minimum grade of C or NEIU Math Placement Result 30 or ACT Math 22 or ACT Math 23 or ACT Math 24 or Accuplacer College Level Math-020 or Accuplacer College Level Math-021 or Accuplacer College Level Math-022 or Accuplacer College Level Math-023 or Accuplacer College Level Math-024 or Accuplacer College Level Math-025 or Accuplacer College Level Math-026 or Accuplacer College Level Math-027 or Accuplacer College Level Math-028 or Accuplacer College Level Math-029 or Accuplacer College Level Math-030.**Corequisite: ** CHEM-108.

**MATH-301. Ordinary Differential Equations I. 3 Hours.**

An introduction to Ordinary Differential Equations and applications. General first order and second order linear equations and numerical methods.**Prerequisite: ** MATH-203 minimum grade of C.

**MATH-302. Ordinary Differential Equations II. 3 Hours.**

Linear and nonlinear systems, matrix methods and applications to problems in the sciences. Existence and stability theory. Boundary value problems and Fourier series.**Prerequisite: ** MATH-301 minimum grade of C.

**MATH-303. Partial Differential Equations. 3 Hours.**

Introduction to partial differential equations and methods of finding solutions.**Prerequisite: ** MATH-301 minimum grade of C.

**MATH-304. Introduction To Numerical Analysis. 3 Hours.**

Solutions of equations of one variable, interpolation and polynomial approximation, numerical integration and methods of solutions of linear systems.**Prerequisites: ** MATH-203 minimum grade of C and MATH-243 minimum grade of C and MATH-340 minimum grade of C.

**MATH-305. Probability And Statistics. 3 Hours.**

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.**Prerequisites: ** MATH-187 minimum grade of C and MATH-251 minimum grade of C.

**MATH-306. Linear Programming And Extensions. 3 Hours.**

Linear programming models; geometric and algebraic foundations of the simplex algortihm; duality theory; the revised and dual algorithms; sensivity analysis; integer programming.**Prerequisites: ** MATH-203 minimum grade of C and MATH-243 minimum grade of C.

**MATH-307. Probability Models For Operations Research. 3 Hours.**

This course focuses on basic mathematical aspects of stochastic models with the emphasis on problem solving. Topics include Markov processes, Markov chains, and Queuing Theory.**Prerequisite: ** MATH-305 minimum grade of C or MATH-334 minimum grade of C.

**MATH-309. Numerical Analysis II. 3 Hours.**

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.**Prerequisite: ** MATH-304 minimum grade of C.

**MATH-312. Foundations Of Geometry. 3 Hours.**

This course is a rigorous study of Euclidean and non-Euclidean geometries. Topics include transformational and projective geometry, axiomatic systems, and models.**Prerequisites: ** MATH-243 minimum grade of C and MATH-251 minimum grade of C.

**MATH-321. History Of Mathematics. 3 Hours.**

Chronological survey of the growth of mathematical ideas, and of famous mathematicians and their contribution to the development of modern mathematics.**Prerequisites: ** MATH-243 minimum grade of C and MATH-251 minimum grade of C.

**MATH-322. Number Theory. 3 Hours.**

This course focuses on integers and their fundamental properties, congruences, quadratic residues, Diophantine equations, primitive roots and discrete logarithms, and cryptography.**Prerequisites:** (MATH-251 minimum grade of C or MATH-311 minimum grade of C) and MATH-253 minimum grade of C.

**MATH-324. Independent Study In Mathematics. 3 Hours.**

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

**MATH-326. Real Analysis. 3 Hours.**

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.**Prerequisite: ** MATH-338 minimum grade of C.

**MATH-328. Complex Variables. 3 Hours.**

Introduction to the functions of a complex variable: Cauchy-reimann equations, Cauchy integral theorems and series expansions.**Prerequisites: ** MATH-338 minimum grade of C and MATH-339 minimum grade of C.

**MATH-331. Abstract Algebra I. 3 Hours.**

This course is an introduction to the mathematical theory of groups. Topics include: properties of groups,homomorphisms, isomorphisms, Lagrange's Theorem and factor groups. Students will build on their basic knowledge of number systems, linear algebra, set theory, functions and mathematical proofs in order to understand, construct and apply algebraic proofs; illustrate algebraic concepts or disprove false statements by providing examples; and calculate with algebraic objects. Applications of algebra and connections between algebra and other fields of mathematical study are emphasized.**Prerequisites: ** MATH-243 minimum grade of C and MATH-251 minimum grade of C.

**MATH-332. Abstract Algebra II. 3 Hours.**

This course is a continuation of MATH-331 with a focus on the mathematical theory of rings and fields. Topics include: ideals, factor rings, finite fields, field extensions, and selected applications. Students will build on their prior knowledge of algebraic systems and algebraic proofs in order to understand, construct, and apply proofs about rings and fields; illustrate ring- and field- theoretic concepts or disprove false statements by providing examples; and calculate with algebraic objects. Applications of algebra and connections between algebra and other fields of mathematical study are emphasized.**Prerequisite: ** MATH-331 minimum grade of C.

**MATH-334. Mathematical Statistics I. 3 Hours.**

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.**Prerequisite: ** MATH-203 minimum grade of C.

**MATH-336. Mathematical Statistics II. 3 Hours.**

Study of estimation procedures including point and interval estimation tests of hypothesis, general procedures for developing tests.**Prerequisite: ** MATH-334 minimum grade of C.

**MATH-337. Theory Of Equations. 3 Hours.**

Study of algebraic equations, existence and properties of solutions; algebraic methods of solution; numeical and algorithmic methods of solution.**Prerequisites: ** MATH-202 minimum grade of C and MATH-251 minimum grade of C.

**MATH-338. Introduction To Real Analysis. 3 Hours.**

This course is an introductory course in the theory of functions of a real variable. It develops the properties of the real numbers as a complete ordered field and introduces the topological concepts of neighborhoods, open sets, closed sets, and compact sets. Based on this, the course provides a rigorous treatment of: a) sequences of real numbers (convergence, boundedness, upper and lower limits); b) real functions of a single variable including continuity, uniform continuity (optional), differentiability, integrability, and related properties; c) series of real numbers (convergence and absolute convergence); d) introduction to function series (power series).**Prerequisites: ** MATH-203 minimum grade of C and (MATH-251 minimum grade of C or MATH-311 minimum grade of C).

**MATH-339. Vector Calculus. 3 Hours.**

This course is a natural extension of differential and integral calculus, where the variables and values of functions are vectors instead of numbers. Such concepts as limits and continuity, derivatives and integrals, extrema and approximation are generalized for multi-dimensional Euclidean spaces. The course also introduces vector fields, line and surface integrals as well as fundamental theorems based on these concepts.**Prerequisites: ** MATH-203 minimum grade of C and MATH-243 minimum grade of C.

**MATH-340. Computing For Mathematicians. 4 Hours.**

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.**Prerequisite: ** MATH-202 minimum grade of C.

**MATH-343. Linear Algebra II. 3 Hours.**

A continuation of MATH-243 with emphasis on computational mehtods and application, LU, QR and SVD Factorizations.**Prerequisites: ** MATH-203 minimum grade of C and MATH-243 minimum grade of C.

**MATH-347. Probability for Actuaries with Actuarial Exam Preparation. 4 Hours.**

This course is a probability class tailored for students/professionals pursuing a career in the actuarial profession (such as, but not limited to, insurance, finance, banking, and industries) and/or are preparing for the actuarial exams. The course provides knowledge of the fundamental probability tools for quantitatively assessing risk and the application of these tools to problems encountered in actuarial science is emphasized. Topics include general probability theory, counting techniques, combinatorial probabilities, random variables with univariate and/or multivariate probability distributions, and The Central Limit Theorem.

**MATH-357. Financial Mathematics for Actuaries with Actuarial Exam Preparation. 4 Hours.**

This course is a financial mathematics class tailored for students/professionals pursuing a career in the actuarial profession (such as, but not limited to, insurance, finance, banking, and industries) and/or are preparing for the actuarial exams. The course provides an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows such as, loans, annuities, rate of return of an investment, bonds, stocks, and financial derivatives.

**MATH-361. Set Theory. 3 Hours.**

**MATH-362. Metric Spaces And Topology. 3 Hours.**

This course is an introduction to topological spaces with an emphasis on metric spaces. The covered topics include open neighborhoods, limits, closure/interior/boundary of topological/metric spaces; functions, continuity, homeomorphism between topological/metric spaces; and product of topological/metric spaces. The concepts of connectedness, compactness, and completeness will be studied along with fundamental results and examples. This course forms a foundation for all advanced courses in analysis and geometry.**Prerequisite:** (MATH-251 minimum grade of C or MATH-311 minimum grade of C)

**MATH-365. Statistical Computer And Data Analysis Packages. 3 Hours.**

Study of topics from current statistical packages such as SAS, SPSS, BMDP and MINITAB.**Prerequisites: ** MATH-334 minimum grade of C and MATH-340 minimum grade of C.

**MATH-370. Mathematical Modeling In The Natural Sciences. 4 Hours.**

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.**Prerequisite: ** MATH-202 minimum grade of D.

**MATH-374. Modeling And Simulations Of Complex Systems Networks. 4 Hours.**

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 as well as construction and analysis of 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 analysis and simulations of individuals, in space, over time to understand how macro-level distribution patterns of outcomes may emerge from explicitly modeled, 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.**Prerequisites: ** MATH-202 minimum grade of C and (MATH-275 minimum grade of C or MATH-273 minimum grade of C).

**MATH-380. Calculus Concepts For Middle School Teachers. 4 Hours.**

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, limits and derivatives, differential equations, polynomials, applications, integration, series, fundamental theorem of calculus. This course is integrated with NEIU BIO-299.

**MATH-381. Concepts In Discrete Mathematics For Middle School Teachers. 3 Hours.**

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.**Prerequisite: ** MATH-380 minimum grade of C or MATH-199X minimum grade of C.

**MATH-406. Linear Programming: Theory And Practice. 3 Hours.**

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. 3 Hours.**

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. 3 Hours.**

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.**Prerequisite: ** MATH-408 minimum grade of C.

**MATH-410. Modern Analysis For The Elementary School Teacher. 3 Hours.**

Limits and continuity, derivatives, applications, integral calculus, applications.**Prerequisite: ** MATH-435 minimum grade of C.

**MATH-421. Modern Geometry. 3 Hours.**

Classification of geometrical systems; introduction to Euclidean and non-Euclidean geometries, projective geometry; finite geometries.**Prerequisite: ** MATH-312 minimum grade of C.

**MATH-430. Discrete Mathematical Structures. 3 Hours.**

Provides a working knowldge of mathematical logic, sets, relations, functions, graphs, and counting techniques.

**MATH-435. Mathematics Structure II. 3 Hours.**

The real number system, mathematical systems, inductive and deductive methods, permutations and combinations.**Prerequisite: ** MATH-408 minimum grade of C.

**MATH-436. Modern Algebra. 3 Hours.**

**Prerequisite: ** MATH-331 minimum grade of C.

**MATH-439. Computers In Education. 3 Hours.**

Investigation into the use of computers for CAI, statistical packages and solutions of mathematical problems. Students learn to write programs in Basic.**Prerequisite: ** MATH-438 minimum grade of C.

**MATH-441. Multivariate Statistical Analysis. 3 Hours.**

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.**Prerequisite: ** MATH-336 minimum grade of C.

**MATH-442. Applied Regression Analysis. 3 Hours.**

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.**Prerequisite: ** MATH-336 minimum grade of C.

**MATH-443. Experimental Design. 3 Hours.**

One-way and two-way analysis of variance, fixed and random effects models, multiple comparisons, completely randomized and randomized block designs.**Prerequisite: ** MATH-336 minimum grade of C.

**MATH-457. Recent Trends In Mathematics. 3 Hours.**

Extended applications of mathematical thinking, operations research, mathematical models, information theory, theory of games, and linear programming.**Prerequisite: ** MATH-435 minimum grade of C.

**MATH-465. Advanced Topics In Numerical Analysis. 3 Hours.**

This course aims to teach participants advanced theories, algorithms and computational techniques of numerical analysis. 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. Participants will become familiar with the process of solving scientific and engineering problems by applying/modifying numerical algorithms that are implemented in standard software packages, designing new algorithms, conducting analysis on accuracy, efficiency and stability, as well as interpreting computational results through graphics and simulations.**Prerequisite: ** MATH-304 minimum grade of C.

**MATH-466. Galois Theory: Historical And Modern. 3 Hours.**

Classical and modern Galois theory. Cardano's formulas, symmetric polynomials, permutation groups, field extensions, field automorphisms, the fundamental theorem of Galois theory.**Prerequisite: ** MATH-331 minimum grade of C.

**MATH-471. Introduction To Stochastic Models. 3 Hours.**

Markov Chains: the Poisson process; continuous time Markov processes; Renewal Theory; Queuing Theory.**Prerequisite: ** MATH-305 minimum grade of C.

**MATH-472. Simulation Modeling And Analysis. 3 Hours.**

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.**Prerequisite: ** MATH-334 minimum grade of C.

**MATH-473D. Advanced Topics In Operations Research: Decision Theory. 3 Hours.**

**MATH-474. Mathematical Modeling. 3 Hours.**

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. 3 Hours.**

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.**Prerequisites: ** MATH-243 minimum grade of C and MATH-339 minimum grade of C.

**MATH-491. Independent Study In Mathematics. 1 Hour.**

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

**MATH-492. Independent Study In Mathematics. 2 Hours.**

(See MATH-491 for descriptions.).

**MATH-493. Independent Study In Mathematics. 3 Hours.**

(See MATH-491 for descriptions.).

**MATH-495. Project In Mathematics. 3 Hours.**

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.

**MATH-5901. Thesis Hours. 1 Hour.**

Guidance of students conducting research and writing a thesis to fulfill requirements for the Master of Science degree in Mathematics is conducted in this course. Students may register for 1-4 credits per term with 6 credits required for the thesis option of the Master of Science in Mathematics. All MATH-590 credits must be earned within the equivalent of two academic years.

**MATH-5902. Thesis Hours. 2 Hours.**

See course description for MATH-5901.

**MATH-5903. Thesis Hours. 3 Hours.**

See course description for MATH-5901.