The undergraduate program in Mathematics leads to a Bachelor of Arts degree in Mathematics and has been designed to provide the students with options suitable for various career plans. The choice of concentration determines the set of mathematics courses required, as well as those that can be taken as electives. Mathematics Majors at Northeastern Illinois University can choose any of the two concentrations: Concentration in Applied Mathematics and Concentration in Secondary Mathematics.

All students enrolled in Mathematics Major Program have to complete the entire set of required core courses, all of the courses required for a given concentration, as well as some elective courses, for the total of at least 46 credit hours. While each mathematics course has prerequisites, there are no prerequisites for entering the program.

## Undergraduate Programs

- Major in Mathematics (Applied and Secondary Education-Mathematics)
- Elementary Education and Humanities Mathematics Minor
- Minor in Applied Mathematics
- Minor in Mathematical & Statistical Modeling of Complex Systems

# Graduate Programs

- Master of Science in Mathematics (Applied and Secondary Education-Mathematics)
- Master of Arts in Pedagogical Content Knowledge for Teaching Elementary and Middle School Mathematics

Lidia Z. Filus, Ph.D., Professor, Chair

Katherine Bird, Ph.D., Assistant Professor

Sarah Cordell, D.A., Associate Professor

Matthew Graham, Ph.D., Assistant Professor

P. Wagala Gwanyama, Ph.D., Professor

Joseph E. Hibdon, Ph.D., Assistant Professor

Nabil Kahouadji, Ph D., Assistant Professor

Anna Mitina, Ph.D., Professor

Marina Polyashuk, Ph.D., Associate Professor

Shan Wang, Ph.D., Assistant Professor

Nancy Wrinkle, Ph.D., Associate Professor

Zhonggang Zeng, Ph.D., Professor

**MATH-090. Elementary Algebra. 3 Hours.**

This course develops the foundations of algebra, beginning with the real number system and its operations. Topics include: variable expressions, linear equations, exponents and polynomials, applications of proportion, percent, and the use of formulas to develop problem solving skills. Freshman students are initially placed into mathematics courses by their MATH ACT scores, their NEIU Mathematics Placement Test scores, or by an appropriate score on the Advanced Placement Test in Calculus. (This course does not count toward graduation or GPA.).

**MATH-0901. Math Enrichment Workshop For Math 090. 1 Hour.**

Mathematics enrichment workshop for students currently enrolled in MATH-090. 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 090 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-090.

**MATH-091. Intermediate Algebra I. 3 Hours.**

This course develops the foundations of algebra, beginning with the real number system and its operations. Topics include: variable expressions, linear equations and systems of equations, exponents, polynomials, factoring trinomials, and solving equations by factoring. Freshman students are initially placed into mathematics courses by their MATH ACT scores, their NEIU Mathematics Placement Test scores, or by an appropriate score on the Advanced Placement Test in Calculus. (This course does not count toward graduation of GPA.).

**MATH-0911. Math Enrichment Workshop For Math 091. 1 Hour.**

Mathematics enrichment workshop for students currently enrolled in MATH-091. 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 091 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-091.

**MATH-092. Intermediate Algebra II. 3 Hours.**

This course further develops the concepts and structures of intermediate algebra. A review of linear equations, polynomials, and factoring, prepares students for the study of linear, quadratic, exponential, and logarithmic equations and functions. Additional topics to prepare students for college algebra include: rational expressions and equations, complex numbers, rational exponents, graphing and applications of quadratic functions, and properties of logarithms. Freshman students are initially placed into mathematics courses by MATH ACT scores, NEIU Mathematics Placement Test scores, or by an appropriate score on the Advanced Placement Test in Calculus. (This course does not count toward graduation or GPA.).

**MATH-0921. Math Enrichment Workshop For Math 092. 1 Hour.**

Mathematics enrichment workshop for students currently enrolled in MATH-092. 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 092 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-092.

**MATH-097. Mathematical Literacy. 4 Hours.**

Mathematical Literacy for College Students is a one semester course for non-math and non-science majors integrating numeracy, proportional reasoning, algebraic reasoning, and functions. Students will develop conceptual and procedural tools that support the use of key mathematical concepts in a variety of contexts. Throughout the course, college success content will be integrated with mathematical topics. Upon passing this course, one can enroll in Math 112 (Statistics) or Math 113 (Mathematical Reasoning). (This course is in place of the Math 091/092 sequence and has no college credit).

**MATH-101A. Basic Mathematical Reasoning 1. 2 Hours.**

This first part of a two-semester stretch course (equivalent to Math 113) 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 variety of fields, such as psychology, economics, finance, sociology and political science. The course is taught in a computer laboratory environment, where students are introduced to tools for data analysis and presentation. Active learning and reasoning are emphasized. By completing Math 101A and 101B, students needing one credit math course will have completed their math requirement.

**MATH-101B. Basic Mathematical Reasoning 2. 2 Hours.**

This second part of a two-semester stretch course (equivalent to Math 113) 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 variety of fields, such as psychology, economics, finance, sociology and political science. The course is taught in a computer laboratory environment, where students are introduced to tools for data analysis and presentation. Active learning and reasoning are emphasized. By completing Math 101A and 101B, students needing one credit math course will have completed their math requirement.**Prerequisite: ** MATH-101A minimum grade of C.

**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.

**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.

**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.

**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.

**MATH-145. Algebra Concepts For Educators. 4 Hours.**

This course focuses on algebra concepts and is designed to meet the needs of educators. Some of the concepts 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 the NCTM teacher standards, Common Core Mathematical Practices, content and ELA Standards in Mathematics and the ISBE mathematics teacher standards and the content and pedagogy necessary to prepare teachers to be developmentally responsive teachers of math and science. Course is linked and integrated with the MSTQE Bios 110.**Prerequisite: ** MATH-150 minimum grade of C or MATH-151 minimum grade of C.**Corequisite: ** BIO-199.

**MATH-147. Statistical Concepts For Educators. 4 Hours.**

This course has been designed keeping in mind the NCTM teacher standards, Common Core Mathematical Practices, Content and ELA Standards in Mathematics and the ISBE mathematics teacher 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-105Environmental 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.

**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.

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

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

**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.

**MATH-173W. College Algebra & Math Enrichment Workshop. 4 Hours.**

This course emphasizes the concept of a function as a unifying approach to the topics of college algebra. Topics include: polynomial, rational, exponential and logarithmic functions, conic sections,

sequences, and series. Each week students will participate in an enrichment workshop where they will collaboratively solve college algebra problems within peer groups while receiving guidance from a Peer Leader. The workshop draws on the Peer Led Team Learning and Emerging Scholars Program models, which have been nationally identified for increasing students' probability of earning higher grades in their mathematics courses. Students will pay a $25 fee to support the workshop.

**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.

**MATH-175W. Trigonometry & Math Enrichment Workshop. 3 Hours.**

This course uses the concept of a function as a unifying approach to the topics of trigonometry. Topics

include: trigonometric functions, identities, and equations, inverse trigonometric functions, solving

triangles, and polar coordinates. Each week students will participate in an enrichment workshop where they will collaboratively solve trigonometry problems within peer groups while receiving guidance from a Peer Leader. The workshop draws on the Peer Led Team Learning and Emerging Scholars Program models, which have been nationally identified for increasing students' probability of earning higher grades in their mathematics courses. Students will pay a $25 fee to support the workshop.

**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.

**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.

**MATH-185W. Precalculus & Math Enrichment Workshop. 4 Hours.**

This course offers a functional approach to college algebra and trigonometry, for students who intend

to continue with Calculus I. Each week students will participate in an enrichment workshop where they will collaboratively solve precalculus problems within peer groups while receiving guidance from a Peer Leader. The workshop draws on the Peer Led Team Learning and Emerging Scholars Program models, which have been nationally identified for increasing students' probability of earning higher grades in their mathematics courses. Students will pay a $25 fee to support the workshop.

**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.

**MATH-187W. Calculus I & Math Enrichment Workshop. 4 Hours.**

This course provides an introduction to analytic geometry, limits and derivatives, integration, and the fundamental theorem of calculus. Each week students will participate in an enrichment workshop where they will collaboratively solve calculus I problems within peer groups while receiving guidance from a Peer Leader. The workshop draws on the Peer Led Team Learning and Emerging Scholars Program models, which have been nationally identified for increasing students' probability of earning higher grades in their mathematics courses. Students will pay a $25 fee to support the workshop.**Prerequisites: ** MATH-173 minimum grade of C and MATH-175 minimum grade of C.

**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.

**MATH-202W. Calculus II & Math Enrichment Workshop. 4 Hours.**

This course provides an introduction to analytic geometry, limits and derivatives, integration, and the

fundamental theorem of calculus. Each week students will participate in an enrichment workshop where they will collaboratively solve calculus II problems within peer groups while receiving guidance from a Peer Leader. The workshop draws on the Peer Led Team Learning and Emerging Scholars Program models, which have been nationally identified for increasing students' probability of earning higher grades in their mathematics courses. Students will pay a $25 fee to support the workshop.**Prerequisite: ** MATH-187 minimum grade of C or MATH-107 minimum grade of C.

**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-203W. Calculus III & Math Enrichment Workshop. 4 Hours.**

This course focuses on three-dimensional analytic geometry, partial derivatives and multiple integrals. Each week students will participate in an enrichment workshop where they will collaboratively solve calculus III problems within peer groups while receiving guidance from a Peer Leader. The workshop draws on the Peer Led Team Learning and Emerging Scholars Program models, which have been nationally identified for increasing students' probability of earning higher grades in their mathematics courses. Students will pay a $25 fee to support the workshop.**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-251W. Introduction To Advanced Mathematics & Math Enrichment Workshop. 5 Hours.**

Math 251 is a bridge course between calculus and advanced mathematics. Students study the tools and proof techniques that serve as the basis for theoretical mathematics. Each week students will participate in an enrichment workshop where they will collaboratively solve Math 251 problems within peer groups while receiving guidance from a Peer Leader. The workshop draws on the Peer Led Team Learning and Emerging Scholars Program models, which have been nationally identified for increasing students' probability of earning higher grades in their mathematics courses. Students will pay a $25 fee to support the workshop.**Prerequisite: ** MATH-187 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.**

This course covers matrix theory and linear algebra. Linear algebra is the branch of mathematics that studies systems of linear equations and the properties of matrices, which includes among other topics: vector spaces; linear transformations and the matrices that represent them; determinants and inner product spaces; and properties of vectors in n-dimensional space and their applications. Linear algebra has a broad range of applications and is critical to many disciplines such as physics, the social and natural sciences, engineering, and economics.**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.**

**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 Educators. 4 Hours.**

This course focuses on the concepts of plane and solid geometry and trigonometry. It is designed to meet the needs of math teachers in accordance with the NCTM teacher standards, Common Core

Mathematical Practices, Content and ELA Standards in Mathematics and the ISBE mathematics teacher 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 manipulatives, 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 Educators. 4 Hours.**

This course has been designed keeping in mind the NCTM teacher standards, Common Core Mathematical Practices, Content and ELA Standards in Mathematics and the ISBE mathematics teacher standards and the content and pedagogy necessary to prepare teachers to be 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-300. Interdisciplinary Seminar In STEM. 2 Hours.**

This course uses a hands-on approach to modern inquiry-based research problems and techniques in the physical and computational sciences. The course is structured around a series of modular problem-based exercises, covering topics from the fields of Chemistry, Computer Science, Earth Science, Mathematics and Physics and is designed to provide the content and pedagogical background for students to be successful peer leaders. The cross-disciplinary modules will draw connections between scientific disciplines, and showcase common research tools and techniques used in the sciences. The workshop will also incorporate discussions on a range of topics, from scientific ethics, scientific methodology and error analysis.**Prerequisite: ** MATH-185 minimum grade of C.

**MATH-301. Ordinary Differential Equations I. 4 Hours.**

This course focuses on the techniques and applications of solving ordinary differentials equations, with a focus on first and second order differential equations. Topics include: constant coefficients, nonlinear, numerical methods, Laplace transform, series solutions, and geometric techniques.**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-253 minimum grade of C and MATH-340 minimum grade of C.

**MATH-305. Probability And Statistics. 4 Hours.**

This course is an introduction to probability and statistics. Topics include fundamental rules of probability, discrete and continuous distributions of random variables, Central Limit Theorem, descriptive statistics, confidence intervals, and hypothesis testing. Students will build on their basic knowledge of probabilities and distributions; illustrate statistical inference by constructing confidence intervals and performing hypothesis testing; and conduct basic statistical analysis manually and by computer software. Applications of probability and connections between probability and statistics are emphasized.**Prerequisite: ** MATH-202 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-253 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-311. 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-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-253 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-253 minimum grade of C and MATH-251 minimum grade of C.

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

Properties of rational integers, congruences, quadratic residues and Diophantine equations.**Prerequisites: ** MATH-251 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-251 minimum grade of C and MATH-253 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. Statistical Inference. 4 Hours.**

Statistical inference is the process of drawing conclusions about populations or scientific truths from data. This course presents the fundamentals of inference in a practical approach for statistical analysis procedures, such as interval estimation, tests of hypothesis, general procedures for developing tests, analyzing different types of data, and linear regression. After taking this course, students will understand the broad directions of statistical inference and use this information for making informed choices in analyzing data using computer software.**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.

**MATH-339. Vector Calculus. 4 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-253 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-253 minimum grade of C.

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

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

**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-371. Mathematical Modeling For Cancer Risk Assessment. 4 Hours.**

The Cancer Modeling Seminar is an essential component of the education of students from the Complex Systems minor and bio mathematical field in general. The Seminar consists of lecture, research projects, interdisciplinary collaborations, presentations, and conference trips. Students will experience first-hand the research process and are expected to contribute, discuss and present their projects under the guidance of the seminar instructor and experts from the oncological field. Students will also learn advanced, high-quality typesetting systems designed for technical and scientific documentation and presentation.**Prerequisite: ** MATH-202 minimum grade of C.

**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-376. Introduction To Risk Analysis. 3 Hours.**

The Introduction to Risk Analysis course is an applied method course focusing on the application of statistical analysis methods on economics using Risk Analysis approaches. Topics include but not limited to basic concepts of risk analysis, probability theory, probabilistic modeling and application to research projects.**Prerequisite: ** MATH-187 minimum grade of C.

**MATH-380. Calculus Concepts For Educators. 4 Hours.**

Course is designed keeping in mind the NCTM teacher standards, Common Core Mathematical Practices, Content and ELA Standards in Mathematics and the ISBE mathematics teacher standards and the understanding that many of the students are preparing to be mathematics teachers. Course emphasis is on developmentally responsive 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 not 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 Educators. 3 Hours.**

Designed especially for 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 developmentally responsive 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-432. Applied Combinatorics. 3 Hours.**

The course offers broad exposure to combinatorial mathematics using applications to emphasize fundamental concepts and techniques, including graph theory, inclusion/exclusion principle, graph algorithms, and network flows.**Requirement:** Admission to MS in Mathematics program or approval of the instructor or graduate advisor in the math department.

**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-444. Problem Solving, Modeling, And Project In Mathematics With Technology. 4 Hours.**

This course is problem solving and project oriented, and provides the students with the background in computers and technology needed to be effective teachers of mathematics in the secondary/high schools. The course deals with (1) hands-on applications of (a) a current geometric visualization software (e.g., Geometer's Sketchpad ) as a problem solving tool in mathematics and geometry, (b) a statistical package (e.g., Minitab, R) as a problem solving tool in mathematics and statistics, and (c) other technologies (e.g., excel software) as a tool for modeling in mathematics and statistics; and (2) introduction to research methods in the mathematical sciences.

**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-253 minimum grade of C and MATH-339 minimum grade of C.

**MATH-477. Risk Analysis. 3 Hours.**

This course introduces students to the application of statistical analysis in economics using risk analysis. Students will use probability theory, probabilistic modeling, and statistical tools to analyze case studies and current research in risk analysis.

**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 2 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.