**MATH 011A - Developmental Stretch I: Statistics in Daily Life. 2 Hours**

Math 011A must be taken concurrently with Math 111A. These two courses comprise the first semester in a two semester sequence. Students completing each of Math 011A, 011B, 111A, and 111B with a C or better will have satisfied the Math 112 requirement and earned a total of 4 college credits. These courses comprise an elementary introduction to statistics. Students will learn: to process and classify observational, experimental, and sampling data; to make decisions using descriptive statistics; to use inferential statistics to test hypotheses and draw conclusions about a population; and to use spreadsheets to perform these tasks.

**MATH 011B - Developmental Stretch II: Statistics in Daily Life. 2 Hours**

Math 011B must be taken concurrently with Math 111B. These two courses comprise the second semester in a two semester sequence. Students completing each of Math 011A, 011B, 111A, and 111B with a C or better will have satisfied the Math 112 requirement and earned a total of 4 college credits. These courses comprise an elementary introduction to statistics. Students will learn: to process and classify observational, experimental, and sampling data; to make decisions using descriptive statistics; to use inferential statistics to test hypotheses and draw conclusions about a population; and to use spreadsheets to perform these tasks.

**MATH 048A - Developmental Stretch I: Math for Elementary Teachers I. 3 Hours**

Math 048A must be taken concurrently with Math 148A. These two courses comprise the first semester in a two semester sequence. Students completing each of Math 048A, 048B, 148A, and 148B with a C or better will have satisfied the Math 149 requirement and earned a total of 4 college credits. These courses comprise a mathematical introduction for elementary and middle school teachers. Topics include place value, models for and the development of arithmetic, mental math, estimation, word problems, algorithms, factors, primes, proofs, pre-algebra, fractions, ratios, rates, and percentages. The development of elementary mathematics from an advanced standpoint is emphasized.

**MATH 048B - Developmental Stretch II: Math for Elementary Teachers I. 3 Hours**

Math 048B must be taken concurrently with Math 148B. These two courses comprise the second semester in a two semester sequence. Students completing each of Math 048A, 048B, 148A, and 148B with a C or better will have satisfied the Math 149 requirement and earned a total of 4 college credits. These courses comprise a mathematical introduction for elementary and middle school teachers. Topics include place value, models for and the development of arithmetic, mental math, estimation, word problems, algorithms, factors, primes, proofs, pre-algebra, fractions, ratios, rates, and percentages. The development of elementary mathematics from an advanced standpoint is emphasized.

**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 and inequalities, exponents and polynomials, factoring, the rectangular coordinate system, and graphing linear equations. Applications of proportion, percent, and the use of formula develop problem solving skills.

**Prerequisite: **NEIU Math Placement Result 00 - 40 or ACT Math 01 - 36 or Accuplacer Elementary Algebra 20 - 40 or Accuplacer QRAS 200 - 236.

**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 focuses on the concepts and structures of intermediate algebra. Topics include linear equations and inequalities, interval notation, graphing linear equations in two variables, slope of a line, equations of a line, polynomials, factoring, systems of linear equations, and rational expressions.

**Prerequisite: **MATH-090 or NEIU Math Placement Result 01-45 or ACT Math 17 - 18 or Accuplacer Elementary Algebra 41 - 45 or Accuplacer QRAS 237-249.

**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, and properties of logarithms.

**Prerequisite: **MATH-091 - 499 or MATH-091A - 499Z or NEIU Math Placement Result 02-45 or ACT Math 19 - 36 or Accuplacer Elementary Algebra 060-084 or Accuplacer College Level Math 020-120 or Accuplacer AAF 200 - 235.

**Corequisite:** MATH-173C.

**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 092C - College Algebra Express I. 3 Hours**

MATH 092C College Algebra Express I must be taken concurrently with Math 173C College Algebra Express II. Math 092C and Math 173C are collectively a 6-credit co-requisite course that provides students a path to finish developmental coursework and college algebra in ONE semester. Background topics which are necessary for a student to successfully complete Math 173C will be covered in Math 092C. Such topics include fractions, factoring polynomials, functions, exponents, and operating with radical and rational expressions. Students who complete MATH 173C with a minimum grade of C will have satisfied the college algebra requirement.

**Corequisite:** MATH-173C.

**MATH 097 - Mathematical Literacy for College Students. 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. This course does not count toward graduation or GPA).

**Prerequisite: **MATH-090 - 499 or MATH-090A - 499Z or ACT Math 17 - 36 or Accuplacer Elementary Algebra 041 - 120.

**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.

**Prerequisite: **ACT Math 17- 36 or Accuplacer Elementary Algebra 041 - 120.

**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 111A - Stretch I: Statistics in Daily Life. 2 Hours**

Math 111A must be taken concurrently with Math 011A. These two courses comprise the first semester in a two semester sequence. Students completing each of Math 011A, 011B, 111A, and 111B with a C or better will have satisfied the Math 112 requirement and earned a total of 4 college credits. These courses comprise an elementary introduction to statistics. Students will learn: to process and classify observational, experimental, and sampling data; to make decisions using descriptive statistics; to use inferential statistics to test hypotheses and draw conclusions about a population; and to use spreadsheets to perform these tasks.

**MATH 111B - Stretch II: Statistics in Daily Life. 2 Hours**

Math 111B must be taken concurrently with Math 011B. These two courses comprise the second semester in a two semester sequence. Students completing each of Math 011A, 011B, 111A, and 111B with a C or better will have satisfied the Math 112 requirement and earned a total of 4 college credits. These courses comprise an elementary introduction to statistics. Students will learn: to process and classify observational, experimental, and sampling data; to make decisions using descriptive statistics; to use inferential statistics to test hypotheses and draw conclusions about a population; and to use spreadsheets to perform these tasks.

**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-092 - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120 or Accuplacer AAF 236 - 249.

**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 integral part of the course. Students write critiques of quantitative arguments, gather data and present arguments based on their analysis.

**Prerequisite: **MATH092- 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120 or Accuplacer AAF 236 - 249.

**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-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 - 24 or Accuplacer College Level Math 020 - 030.

**Corequisite: **BIO-104, BIO-105.

**MATH 148A - Stretch I: Math for Elementary Teachers I. 2 Hours**

Math 148A must be taken concurrently with Math 048A. These two courses comprise the fist semester in a two semester sequence. Students completing each of Math 048A, 048B, 148A, and 148B with a C or better will have satisfied the Math 149 requirement and earned a total of 4 college credits. These courses comprise a mathematical introduction for elementary and middle school teachers. Topics include place value, models for and the development of arithmetic, mental math, estimation, word problems, algorithms, factors, primes, proofs, pre-algebra, fractions, ratios, rates, and percentages. The development of elementary mathematics from an advanced standpoint is emphasized.

**MATH 148B - Stretch II: Math for Elementary Teachers I. 2 Hours**

Math 148B must be taken concurrently with Math 048B. These two courses comprise the second semester in a two semester sequence. Students completing each of Math 048A, 048B, 148A, and 148B with a C or better will have satisfied the Math 149 requirement and earned a total of 4 college credits. These courses comprise a mathematical introduction for elementary and middle school teachers. Topics include place value, models for and the development of arithmetic, mental math, estimation, word problems, algorithms, factors, primes, proofs, pre-algebra, fractions, ratios, rates, and percentages. The development of elementary mathematics from an advanced standpoint is emphasized.

**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, pre-algebra, fractions, ratios, rates, and percentages. Emphasis on the development of elementary mathematics from an advanced standpoint.

**Prerequisite: **MATH-092 minimum grade of C or Accuplacer AAF 236 - 249.

**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-149minimum 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 Algebra level, is designed to provide quantitative understanding and tools for business students. Students work extensively with the most important functions and equations used for applications in their fields: linear, polynomial, rational, exponential, and logarithmic.

**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 or Accuplacer AAF 236 - 249.

**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 MATH-173 or NEIU Math Placement Result 35 - 40 or ACT Math 25 - 36 or Accuplacer College Level Math 031 - 120 or Accuplacer AAF 250 - 275.

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

Elements of analytic geometry, differential 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 or Accuplacer 250 - 275.

**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: **MATH092- 499 or MATH-092A - 499Z or NEIU Math Placement Result 30 - 40 or ACT Math 22 - 36 or Accuplacer College Level Math-020 - 120 or Accuplacer AAF 236 - 249.

**MATH 173C - College Algebra Express II. 4 Hours**

MATH 173C College Algebra Express II must be taken concurrently with Math 092C College Algebra Express I. Math 092C and Math 173C are collectively a 7-credit co-requisite course that provides students a path to finish developmental coursework and college algebra in ONE semester. This course is a functional approach to algebra that emphasizes the study of functions and their graphs, inequalities, and linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions. Appropriate applications and technologies will be included. Students who complete the co-requisite MATH 173C with a minimum grade of C will have satisfied the college algebra requirement.

**Corequisite: **MATH-092C.

**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 or Accuplacer AAF 236 - 249.

**MATH 175W - 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.

**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 or Accuplacer AAF 236 - 249.

**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 or Accuplacer AAF 250 - 275.

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

Introduction 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 202 - Calculus II. 4 Hours**

Integration techniques, applications, differential equations and series.

**Prerequisite:** MATH-187 minimum grade of C or MATH-107 minimum grade of C 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 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.

**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 solid 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 - 24 or Accuplacer College Level Math-020 - 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 - 24 or Accuplacer College Level Math 020 - 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. 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.**

This course continues the discussion and analysis of Ordinary Differential Equations I. The topics include the analysis of linear and nonlinear system of differential equations, stability calculations of differential equations, and the Sturm-Liouville Theorem. The course also covers an introduction of boundary value problems, Fourier series, and partial differential equations. Applications of differential equations are emphasized throughout the course.

**Prerequisite: ** MATH-301 minimum grade of C.

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

This course covers linear partial differential equations that model physical problems and arise in a variety of contexts. Topics include the study of explicit formulas for solutions (when feasible) and study of the behavior of solutions. Equations covered include: wave equations, diffusion equations, and Laplace’s equation on different domains. Other topics discussed are Fourier series, separation of variables, harmonic functions, and Green’s functions.

**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. 3 Hours.**

This course is an introduction to the 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 tests. Students will build on their basic knowledge of probabilities and distributions; illustrate statistical inference by constructing confidence intervals and hypothesis tests; and calculate basic statistical analysis manually and by computer software. Applications of probability and connections between probability and statistics are emphasized.

**Prerequisites: ** MATH-202 minimum grade of C or (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 algorithm; duality theory; the revised and dual algorithms; sensitivity 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 or MATH-311 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 or MATH-311 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.**

This course offers students an opportunity to conduct an individualized investigation into a mathematical topic with a mathematics department faculty. The mathematical topic is a topic that would not normally be discussed in the current courses being offered by the math department. The course requires the approval of the instructor, department chair, and the Dean.

**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.**

This course is an introduction to the functions of a complex variable. Topics include elementary functions of a complex variable, Cauchy-Riemann Equations, Cauchy integral theorems, Taylor and Laurent series expansions, contour integrals, and residue calculus.

**Prerequisites: **MATH-203 minimum grade of B and MATH-338 minimum grade of C or consent of Instructor.

**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 or MATH 311 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.**

This course is an introduction to probability and mathematical statistics. Topics include fundamental rules of probability, expectations, moment generating functions, common distributions and central limit theorem. The mathematical theories to develop probability and statistical methods are emphasized in this course.

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

**MATH 336 - Mathematical Statistics II. 3 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-305 minimum grade of C or MATH-334 minimum grade of C.

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

This course is an advanced study of algebraic equations. Topics include the existence and properties of solutions, and algebraic, numerical, and algorithmic methods of solving equations.

**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-253 minimum grade of C.

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

Fundamentals of computer 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.**

Linear Algebra arose from studying systems of linear equations and their geometric applications. Linear Algebra is the study of vector spaces and the linear maps between them. This second course in Linear Algebra will emphasize theoretical implications and will focus on “why” and “how” questions, such as how can we use eigenvectors and eigenvalues of a linear operator to study the operator itself and the vector space that it acts on. Particular topics that will be covered are: abstract vector spaces; invariant subspaces; Spectral Theorem; LU, QR, and SVD factorizations; Jordan Form; and various computational methods..

**Prerequisites: ** MATH-203 minimum grade of C and MATH-253 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.

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

**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.

**Prerequisites: **MATH-347 minimum grade of C or MATH-305 minimum grade of C or MATH-334 minimum grade of C.

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

Set theory is one language/structure that mathematics is constructed within. In this course a brief, but rigorous, history of set theory will be given that pays particular attention to the necessary modifications that have been made throughout the twentieth century. Particular attention will be paid to understanding the Axiom of Choice, Zorn’s Lemma, and the Well Ordering Principle. Additional topics might include gentle introductions to Category Theory, Topos Theory, Axiomatic Set Theory, or Godel’s Incompleteness theorem.

**Prerequisites: **MATH-251 minimum grade of C or MATH-311 minimum grade of C.

**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.**

This course introduces statistical programming packages R and SPSS. Students will use the statistical software to: study basic functions and graphs; give descriptive analysis; implement testing; and study various modeling techniques.

**Prerequisites: **MATH-305 minimum grade of C and MATH-334 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 C.

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

The Cancer Modeling Seminar is an essential educational component for students from the Complex Systems minor, Physics, Chemistry and Biomathematics. The seminar consists of lectures, research projects, interdisciplinary collaborations, presentations and/or posters and conference trips. Students will experience first-hand the research process, employ data analysis tools, contribute, discuss and present their projects under the guidance of the seminar instructor and experts in cancer research. 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 375 - 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 are not limited to basic concepts of risk analysis, probability theory, probabilistic modeling and application to research projects.

**Prerequisites: **MATH-187 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 386 - Seminar On Belief Systems In Math And Science. 3 Hours.**

At the core of doing mathematics and science is the ability to update one’s belief. In this seminar students will be exposed to: how both mathematicians and scientists update their beliefs; how Bayesian statistics fit into this process; many different fallacies such as positive bias, fundamental attribution error, etc.; and cognitive psychology that describes the inner workings of the brain that make all of these things happen. The students will then use these structures and vocabulary to explore how this knowledge should inform their teaching perspectives and practices.

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

Optimization models; theoretical foundations of simplex algorithms and duality; revised and dual algorithms; sensitivity and analysis; additional topics from extended LP integer 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 knowledge 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. Experimental Design. 3 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 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 concentration. Students present both written and oral reports to the department.

**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.