## Mathematics

## Who is a Mathematician?

This is not an easy question to answer. The tasks assigned to mathematicians are usually as diverse as the companies that employ them. Mathematicians are frequently assigned to serve as mathematical consultants within teams of other specialists (engineers, accountants, sociologist, to name a few) and they are often part of a scientific team. A mathematician’s exposure to diverse areas of mathematics (calculus and non-calculus based analysis, numerical analysis, statistics, operations research), he or she may perform the function of researching and guiding a project group to and through a certain method of analysis. Clearly the increased use of computers has greatly influenced the role of a mathematician. He or she may perform the function of preparing a problem to obtain a solution on computing devices. In many instances this may mean programming on the computer. In other cases the mathematician may never actually see the computer.

## The Challenge of a Career?

In today’s world there is an ongoing effort to quantify many aspects of our society. There is always a need for mathematicians to numerically formulate and solve new problems. There is demand for good applied mathematicians in all areas of our technological world: business, engineering, government, science, and others. People at the helm of mathematics are vital to our progress as a society. Careers for such people are diverse and abundant. A mathematician may be employed in the areas of:

- Statistics
- System Analysis
- Teaching
- Civil Service (Government)
- Actuarial Sciences
- Consulting
- Operations Research
- Industrial Research and Development

## UNDERGRADUATE PROGRAM

**MATHEMATICS (MATH 27.01)**

**MATH 003. Developmental Mathematics II.**3-6-0. Prerequisite: C or better in MATH 002 or satisfactory score on placement test. The real numbers and their properties, linear equations and inequalities, systems of equations, polynomials, fractional expressions and equations, exponents and radicals, quadratic equations, and functions and their graphs. (Credit earned in this course cannot be applied toward a degree.) (32.0104)

**MATH 100. College Algebra.**5-3-4. Prerequisites: C or better in MATH 003 or C or better in MATH 115, or MATH ACT subscore of 19 or better or satisfactory score on placement test. Degree credit will be granted in only one of the following courses: Math 100, Math 101. Linear equations and inequalities, linear applications, systems of linear equations, quadratic equations and inequalities, absolute value equations and inequalities, radical equations, functions and graphs, polynomial and exponential and logarithmic functions. Credit in MATH 100 is equivalent to MATH 101. [LCCN: CMAT 1213] (27.0101)

**MATH 101. College Algebra.**3-2-3. Prerequisite: Grade of C or better in MATH 003, C or better in MATH 115, or Grade of D in MATH 100, or Math ACT Subscore of 21 or better, or satisfactory score on placement test. Linear equations and inequalities, linear applications, systems of linear equations, quadratic equations and inequalities, absolute-value equations and inequalities, radical equations, functions and graphs, polynomial and exponential and logarithmic functions. For MATH 101 WWW (web), priority is given to students enrolling in MATH 101 for the first time. Credit in MATH 100 is equivalent to MATH 101. [LCCN: CMAT 1213] (27.0101)

**MATH 102. Trigonometry.**3-3-0. Prerequisite: C or better in MATH 100 or MATH 101. Trigonometric ratios, circular functions and graphs, solutions of triangles, logarithmic and exponential functions, inverse functions, identities and equations, complex numbers, introduction to analytical geometry. [LCCN: CMAT 1223] (27.0101)

**MATH 106. Calculus with Business and Economic Applications.** 3-3-0. Prerequisite: C or better in MATH 100 or MATH 101. Algebraic, exponential, and logarithmic functions, intuitive limits, derivatives, and applications of the derivative. (27.0101)

**MATH 108. Pre-Calculus.** 4-4-0. Prerequisite: C or better in MATH 102 or minimum Math ACT score of 23. Inequalities, functions, theory of equations, exponential and logarithmic functions; trigonometric functions, analytic geometry. [LCCN: CMAT 1234] (27.0101)

**MATH 110. Mathematics for Elementary Teachers I.** 3-3-0. Restricted to College of Education majors only. Prerequisite: C or better in MATH 100 or MATH 101. Logic and deductive reasoning; patterns, sequences, functions, and problem solving; introductory number theory; the real number system, informal and formal solutions of equations and inequalities. (27.0101)

**MATH 113. Honors Pre-Calculus.** 4-4-0. Prerequisite: ACT math sub-score of 24 or higher. Permission of Honors Director and department head. (27.0101)

**MATH 114. Honors Trigonometry.** 3-3-0. Prerequisite: 24 MATH ACT. Honors based investigation of trigonometric ratios, circular functions and graphs, solutions of triangles, inverse functions, identities and equations. (27.0101)

**MATH 115. Essentials of College Mathematics.** 3-3-0. Co-registration is required in MATH 115L. Prerequisite: ACT mathematics sub-score of 18 or grade of C or better in MATH 002. Essential elements of algebra and statistics, including exponents, radicals, algebraic expressions, ratio, proportion, linear equations, quadratic equations, descriptive statistics, combinations, permutations, and linear regression. (27.0101)

**MATH 115L. Essentials of College Mathematics Lab.** 2-0-3. Co-registration is required in MATH 115. A supplemental instruction/laboratory course to accompany MATH 115. S or U assigned upon completion of course. (Credit earned in this course cannot be applied toward a degree.) (27.0101)

**MATH 116. Contemporary Mathematics and Quantitative Analysis I. **3-3-0. Coregistration is required in MATH 116L. Prerequisite: MATH ACT subscore of 18 or grade of C or better in MATH 002. Degree credit will be granted in only ONE of the following courses: MATH 116, MATH 117. This course applies basic college-level mathematics to real-llife problems and is appropriate for students whose majors do not require college algebra. This course covers selected topics in reasoning, data analysis, financial mathematics, measurement, and applications of mathematics to everyday problem-solving. *Credit in MATH 116 is equivalent to MATH 117.* (27.0101)

**MATH 116L. Contemporary Mathematics and Quantitative Analysis I Lab.** 2-0-3. Coregistration is required in MATH 116. A supplemental instruction/laboratory course to accompany MATH 116. S or U assigned upon completion of course. (Credit earned in this course cannot be applied toward a degree.) (27.0101)

**MATH 117. Contemporary Mathematics and Quantitative Analysis I.** 3-3-0. Prerequisite: Grade of C or better in MATH 003, or 115, grade of D or better in MATH 100 or 101, or MATH ACT subscore of 19 or better, or satisfactory score on placement test. Degree credit will be granted in only one of the following courses: MATH 116, MATH 117. This course applies basic college-level mathematics to real-life problems and is appropriate for students whose majors do not require college algebra. This course covers selected topics in reasoning, data analysis, financial mathematics, measurement, and applications of mathematics to everyday problem-solving. *Credit in MATH 116 is equivalent to MATH 117*. [LCCN: CMAT 1103] (27.0101)

**MATH 118.** **Contemporary Mathematics and Quantitative Analysis II. **3-3-0. Prerequisite: Grade of D or better in MATH 116 or MATH 117. Continuation, extension, and applications of topics from MATH 117, including ratio, proportion, percent and percentages, modeling with algebraic functions, consumer mathematics, elementary graph theory, and probability/statistics. (27.0101)

**MATH 165. Calculus I.** 5-6-0. Prerequisite: C or better in MATH 102 or MATH 108. Limits, derivatives and integrals of algebraic functions, applications of derivatives and integrals. [LCCN: CMAT 2115] (27.0101)

**MATH 166. Calculus II.** 4-5-0. Prerequisite: C or better in MATH 165. Transcendental functions, derivatives, integrals, analytical geometry, infinite series, polar coordinates and vectors in the plane. [LCCN: CMAT 2124] (27.0101)

**MATH 210. Mathematics for Elementary Teachers II.** 3-3-0. Prerequisite: C or better in MATH 110. Introductory probability, introductory statistics, plane figures, measurement, geometric constructions, area, perimeter, tessellations, similarity, congruence, coordinate geometry, mappings and transformations, space figures, volume, surface area, right triangle trigonometry. (27.0101)

**MATH 214. Introductory Statistics.** 3-3-0. Prerequisites: C or better in MATH 100, 101, 115, 116, or 117. Organizing data, averages and variations, stem-and-leaf and box plots and other graphical presentations of data, conducting experiments, elementary probability theory, distributions, estimations, hypothesis testing, regression and correlation. [LCCN: CMAT 1303] (27.0101)

**MATH 261. Discrete Mathematics.** 3-3-0. Prerequisite: MATH 106, 165, or permission of department head. Introduction to logic, set theory, number theory, graph theory, mathematical induction and recursion, groups and semi-groups, and Boolean algebra. MATH 261 cannot be used in place of MATH 358 or for satisfying prerequisite requirements for other mathematics courses. (27.0101)

**MATH 265. Calculus III.** 4-4-0. Prerequisite: C or better in MATH 166. Vectors and parametric equations, partial derivatives, multiple integrals, derivatives and integrals of vector functions, introduction to linear algebra. (27.0101)

**MATH 301. Elementary Statistical Methods I.** 3 3 0. Prerequisite: ENGL 102 and eligibility for MATH 165; or ENGL 102, and C or better in MATH 101, and C or better in at least one of MATH 102 or 106 or 108 or 214. Descriptive statistics, graphical presentation of data, trend and relationship, some probability distributions, central limit theorem, estimation, confidence interval, hypothesis testing, regression and correlation analyses, and non parametric tests. Emphasis on applications and statistical computer packages. (27.0501)

**MATH 313. Topics in Mathematics for the Humanities.** 3-3-0. Prerequisite: Six hours of non-developmental MATH with C or better in each course. Selected mathematical excursions and topics in elementary number theory, algebra, geometry, and probability, with emphasis on liberal arts applications, appreciation, inductive thinking and discovery, mathematical modeling, patern recognition, current technology, and the history of mathematics. Class discussion and exercises. Especially for the non-mathematics major. (27.0101)

**MATH 320. Mathematics for Middle School Teachers.** 3-3-0. Prerequisites: C or better in MATH 101, 110, and 210. Number systems, number sense, operations, quantitative literacy, measurement; representation of functions and other algebraic structures; geometric modeling; elementary game theory; inductive, deductive, and inferential methods of problem-solving; elementary analysis. School site visits required. (27.0101)

**MATH 321. Mathematics for Middle School Teachers Laboratory.** 1-0-2. Co-requisite: MATH 320. Reinforces and applies concepts learned in MATH 320; emphasis on technology, communication, and the use of mathematics in diverse contexts. School site visits required. (27.0101)

**MATH 355. Differential Equations.** 3-3-0. Prerequisite: C or better in MATH 166. Theory and application of ordinary differential equations. (27.0101)

**MATH 358. Foundations of Mathematics.** 3-3-0. Prerequisite: C or better in MATH 166. Logic, sets, methods of mathematical proofs, relations, functions, mappings, ordered fields and their properties, axiomatization of number systems. (27.0101)

**MATH 360. Linear Algebra.** 3-3-0. Prerequisites: C or better in both MATH 265 and MATH 358. The real number system, vectors, matrices, and linear equations, determinants, polynomials and complex numbers, vector spaces and linear transformations. (27.0101)

***MATH 401. Theory of Probability.** 3-3-0. Prerequisite: C or better in MATH 166. Elementary probability theory, random variables, discrete and continuous probability distributions, moments and moment generating functions, functions of random variables, sampling distributions, and the central limit theorem. Fa only. (27.0501)

***MATH 402. Mathematical Statistics.** 3-3-0. Prerequisites: C or better in Math 265, and C or better in MATH 401. Bivariate probability distributions, marginal and conditional distributions, conditional expectations, estimation, point estimators and methods of estimation, confidence interval, hypothesis testing, likelihood ratio tests, comparison of two means and two variances, linear models and estimation by method of least squares, non parametric tests. Sp only. (27.0501)

***MATH 405. Numerical Analysis I.** 3-3-0. Prerequisites: C or better in all of the following: MATH 265, 355, and 360. Numerical solution of equations and systems, convergence theorems, eigenvalue and eigenvector methods, interpolation and extrapolation. Attention to theory with emphasis on methods applicable to high-speed computation. Fa only. (27.0101)

**MATH 407. Mathematical Probability and Statistics.** 3-4-0. Prerequisites: C or better in MATH 265. Course in the theory of statistics and probability based on set theory and calculus. Includes data analysis, discrete and continuous probability distributions, random sampling, and sampling distributions, regression analysis, parameter estimation, hypothesis testing, and analysis of variance. (27.0101)

***MATH 423. Geometry.** 3-3-0. Prerequisite: C or better in MATH 265 and 358. A development of traditional Euclidean and non Euclidean geometries. Fa only. (27.0101)

***MATH 461. Optimization.** 3-3-0. Prerequisite: C or better in MATH 360. Classical and modern techniques in constrained and unconstrained optimization of functions of several variables. Mathematical programming methods and an introduction to calculus of variations. (27.0301)

***MATH 465. Modern Algebra I.** 3-3-0. Prerequisites: C or better in MATH 358 and C or better in Math 360. Introductory concepts, axiomatic approach to the number system, general algebraic systems, groups. Sp only. (27.0101)

***MATH 471. Elementary Topology.** 3-3-0. Prerequisite: C or better in MATH 360. An information and introductory study of topological spaces. (27.0101)

**MATH 481. Principles of Mathematical Analysis I.** 3-3-0. Prerequisites: C or better in MATH 265 and 360. Number systems; completeness axiom; sequences and series of real numbers; functions of a single real variable; continuity and uniform continuity; differentiation; a systematic development of the Riemann integral. (27.0101)

***MATH 482. Principles of Mathematical Analysis II.** 3-3-0. Prerequisite: C or better in MATH 481. Three dimensional theory and applications; infinite series; conformal mappings; partial differential equations. (27.0101)

**MATH 485. Complex Analysis.** 3-3-0. Prerequisites: C or better in all of the following: MATH 265, 355 and 358. Complex numbers, analytic functions, elementary functions, mapping by elementary functions, integrals, power series. (27.0101)

**MATH 488.** **Topics in Mathematics. **3-3-0. Prerequisite: Permission of department head. Selected current topics in mathematics, especially relevant to educators. May be repeated for credit if content differs. (27.0101)

**MATH 491. Mathematical Models.** 3-3-0. Prerequisites: C or better in all of the following: MATH 265, 355 and CMPS 135. The study of various types of mathematical models which arise in biology, management, economics, and physical and social sciences. (27.0301)

**MATH 495. Topics in Advanced Mathematics.** 3-3-0. Prerequisite: Permission of department head. Selected current topics in mathematics. May be repeated for credit if content differs. (27.0101)

**MATH 499. Undergraduate Major Examination.** 0-0-1. Must be scheduled during the final year. S is assigned upon taking the examination; otherwise the student receives a grade of U. (27.999)

**MATH 500. Preparation for Teaching Developmental Mathematics.** 1-1-0. Prerequisite: Graduate assistant in the Department of Mathematics or permission of department head. This seminar course is designed to prepare graduate students, especially those with little formal training as educators, to assume instructional roles as teaching assistants and/or tutors in selected university mathematics courses. Areas of emphasis include facilitation of student learning, effective small-group teaching, instructional etiquette and management, and teaching portfolio development. S or U will be earned upon completion. (Credit earned n this course cannot be applied toward a degree.) (27.0501)

**MATH 507. Biostatistics.** 3-3-0. Prerequisite: MATH 301, 402, or 407. The application of statistical methods and techniques to the study of living organisms and biological systems. Includes experimental design and data analysis, projection methods, descriptive and inferential statistics, and specific computer applications. (26.1102)

**MATH 509. Logic and Foundations of Mathematics.** 3-3-0. Prerequisites: MATH 265 and 358. Cornerstone course normally taken in first semester of graduate study. Developing and evaluating arguments and proofs, the use of various types of reasoning, methods of proof, making and investigating conjectures. (27.0101).

**MATH 510. Number-Theoretic and Discrete Structures.** 3-3-0. Prerequisite or co-requisite: MATH 509. Primes, congruences, algebraic number theory, diophantine equations, and theory of algebraic equations. Applications of the theory of number systems to problem solving. Representation of phenomena via finite graphs, recursive relations, and combinatorial structures. (27.0101)

**MATH 511. Calculus and Analytic Structures.** 3-3-0. Prerequisite or co-requisite: MATH 509. Formal exploration of continuity, limits, derivatives, integrals, sequences, series, basic differential equations, and introductory numerical analysis. Applications of concepts. (27.0101)

**MATH 512. Probability and Statistics.** 3-3-0. Prerequisite: MATH 360, and either MATH 402 or MATH 407. Discrete and continuous probability distributions, measures of variability, estimation, hypothesis testing, prediction, introduction to stochastic modeling and operations research, simple and multiple linear regressions, measures of association and correlation, analysis of variance and its relationship regression analysis. (27.0501)

**MATH 523. Geometric and Algebraic Structures.** 3-3-0. Prerequisite or co-requisite: MATH 509. Examination of the complementary relationships between geometry and algebra, and among the structures in each discipline. Focuses on the interdependence among geometric and algebraic properties of objects. Spatial reasoning, non-Euclidean representations of curves and space, fractal geometry, calculus of higher dimensions. Representation of geometric structures and other phenomena via semigroups, groups, rings, and other algebraic constructs. (27.0101)

**MATH 530. Introduction to Decision Theory.** 3-3-0. Prerequisite: MATH 401 or MATH 407. Topics in decision theory with applications to real world problems. (27.0301)

**MATH 540. Applied Matrix Analysis.** 3-3-0. Prerequisite: MATH 360. Vector spaces and transformations, eigensystems, quadratic forms. (27.0301)

**MATH 557. Applied Analysis I.** 3-3-0. Prerequisite: MATH 358. Vectors; matrices; differential and integral calculus of functions of several variables; differential and integral vector calculus. (27.0301)

**MATH 558. Applied Analysis II.** 3-3-0. Prerequisite: MATH 557. Functions of a complex variable; derivatives; integrals; analytic functions; Cauchy Riemann equations; Cauchy’s integral theorem and formula; power series. (27.0301)

**MATH 570. Mathematical Modeling and Problem Solving.** 3-3-0. Prerequisite: MATH 355, and either MATH 402 or MATH 407. Use of previous course work to construct models for various problems in the sciences, managerial sciences, or other related areas. (27.0301)

**MATH 573. Topics in the History of Mathematics.** 3-3-0. Prerequisite or co-requisite: MATH 509. Selected topics in the history of mathematics. A general survey of mathematics normally includes developments in geometry, algebra, number theory, and calculus as well as biographies of significant mathematicians and their contributions to mathematics and society. May be repeated for credit if content differs. No more than six hours may be counted towards a degree. (27.0101)

**MATH 577. Topics in Mathematics.** 3-3-3. Prerequisite: Permission of department head. Selected current topics in mathematics especially relevant to professional development. May be repeated for credit if content differs. No more than a total of six hours from MATH 577 and/or MATH 588 may be counted as graduate semester content hours in the teaching discipline. (27.0101)

**Math 578. Research in Mathematics Education. **3-3-0. (Not for credit as mathematics content course). Prerequisite or corequisite: MATH 509. Study of basic methods in mathematics education research. Includes experience in research designs, data gathering, analysis, and interpretation. Addresses elements affecting curricular and research agendas in the teaching of mathematics. (27.0199)

**MATH 580. Topics in the School Mathematics Curriculum.** 3-3-0. (Not for credit as mathematics content course). Prerequisite or corequisite: MATH 509. Practices, activities, and delivery methods related to curriculum development, problem solving, and critical thinking. The four focus areas are algebra, geometry, precalculus, and calculus. Standards and guidelines from professional mathematical and educational organizations are examined as rubrics for curriculum development. (27.0101)

**MATH 584. Technology and Communication in Mathematics.** 3-3-0. Prerequisite: MATH 509. Capstone course normally taken in final semester of graduate study. Application of a variety of strategies and use of multiple sources of information and technology to solve problems. Students draw on previous course work as they conduct investigations and present mathematical ideas orally, in writing, and by demonstration. Includes formal and informal presentations in groups or individually. Presentations may occur at off-campus sites. (27.0101)

**MATH 588. Topics in Mathematics.** 6-6-0. Prerequisite: Permission of department head. Selected current topics in mathematics. May be repeated for credit if content differs. No more than a total of six hours from MATH 577 and/or MATH 588 may be counted as graduate semester content hours in the teaching discipline. (27.0101)

**MATH 589. Topics in Graduate Mathematics.** 3-3-0. Prerequisite: Permission of department head. Selected current topics in mathematics. May be repeated for credit if content differs. (27.0101)

**MATH 590. Topics in Graduate Mathematics.** 3-3-0. Prerequisite: Permission of department head. Selected current topics in mathematics. May be repeated for credit if content differs. No student may apply more than six hours toward graduation. (27.0101)

**MATH 595. Master’s Comprehensive Examination.** 0-0-4. Must be scheduled during final semester or session. S or U assigned upon completion of examination. (27.9999)

## Bachelors in Mathematics

The faculty of the Department of Mathematics at Nicholls State University are dedicated to preparing students to adapt to the needs and demands of a technologically oriented society. Our tools are effective instruction combined with sound counseling. Our aim is excellence. Insuring that students achieve excellence is our greatest responsibility. We are interested in each individual student, and in that student’s progress, both academic and personal.

Our Department offers a Bachelor of Science degree in mathematics with concentrations in advanced mathematics, computer science, and secondary education. The core of the program consists in a variety of courses including linear programming, statistics, numerical analysis, and modern algebra.

## Undergraduate Program Coordinator

Dr. Heather Gamel

Email: heather.gamel@nicholls.edu

Phone: 985.448.4380

## CONTACT INFORMATION

**Office Location:**

108 Peltier Hall

**Mailing Address:**

P.O. Box 2026

Thibodaux, Louisiana 70310

**Phone:**985-448-4381

**Fax:**985-448-4374

**E-mail:**Racheal Ledet

**For more information about the program please contact:**

**For more information about the program please contact:**

Dr. Brian Heck, Department Head (Interim), Graduate Program Coordinator

Email: brian.heck@nicholls.edu

Phone: 985.448.4383

Dr. Heather Gamel, Undergraduate Program Coordinator

Email: heather.gamel@nicholls.edu

Phone: 985.448.4380