**Please Note: Students currently registered in a University of Illinois Graduate Degree program will be restricted from registering in 16-week Academic Year-term NetMath courses. Matriculating UIUC Grad students will be allowed to register in Summer Session II NetMath courses.**

This page has information regarding the self-paced, rolling enrollment course. If you are a UIUC student interested in taking a course during the summer, you may be interested in a Summer Session II course.

## MATH 241 - Mathematics

An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections of the course will use the software package MATLAB. Credit will be granted for only one of the following: MATH 241 or MATH 340.

#### Prerequisites

#### Topics

**XI. Vectors, Lines and Planes.**

Cartesian coordinates of space

Vectors

Lines

Planes

Dot and cross product

**XII. Vector-valued Functions**

Vector-valued functions

Tangents

Normals

Curvature

**XIII. Partial Derivatives**

Quadric surfaces

Partial derivatives

Chain rule

Directional derivatives

Gradients

Extreme values

Lagrange multipliers

**XIV. Multiple Integrals**

Double and triple integrals

Change of variable

Volume

Surface area

Moments and centers of gravity

**XV. Calculus of Vector Fields**

Line and surface integrals

Green's theorem

Stokes' theorem

Divergence theorem

## Mathematics (MATH)

Consideration of diverse subjects in mathematics. Content varies from semester to semester with specific subject matter for each course announced just prior to enrollment. Designed for non-majors who wish to study mathematics other than calculus. This is the preferred course for students interested in taking just one mathematics course at the College. One unit.

Common Area: Mathematical Science

Typically Offered: Annually

A version of Mathematics 135 that is designed for students who require more class time to make the transition to college-level mathematics. See the description of Introductory Courses before choosing this course. See the description of Mathematics 135 for the course content. This course meets five hours per week.

Students who have taken MATH 135, MATH 220, BIOL 275, ECON 249, PSYC 200, SOCL 226 may not enroll in this class.

Common Area: Mathematical Science

A version of Mathematics 136 that is designed for students who require more class time to make the transition to college-level mathematics. See the description of Mathematics 136 for the course content. This course meets five hours per week.

Prerequisite: MATH 133 or MATH 135. Students who have earned credit for a course equivalent to Calculus 2 or above cannot enroll in MATH 134.

Common Area: Mathematical Science

This is the standard version of Calculus at the College. Considers the calculus of real-valued functions of one variable for students who are planning further course work in mathematics, a major in the social or physical sciences, or the premedical program. Emphasis is placed on a conceptual understanding of the calculus, presenting material from symbolic, numerical, and graphical points of view. The concepts of limit, continuity, and derivative are developed and applied to algebraic, logarithmic, exponential and trigonometric functions.Applications of the derivative are explored. This course meets three hours per week.

Students who have earned credit for a course equivalent to Calculus 1 or above cannot enroll in MATH 135.

Common Area: Mathematical Science

Typically Offered: Fall, Spring

Considers the calculus of real-valued functions of one variable for students who are planning further course work in mathematics, a major in the social or physical sciences, or the premedical program. Emphasis is placed on a conceptual understanding of the calculus, presenting material from symbolic, numerical, and graphical points of view. Course content include the theory, evaluation, and applications of integration, sequences and series including Taylor polynomials and series, and an introduction to ordinary differential equations. This course is the prerequisite for Mathematics 241. This course meets four hours per week.

Students who have earned credit for a course equivalent to Calculus 2 or above cannot enroll in MATH 136. Intended for students who have completed one year of Calculus at the high school level.

Common Area: Mathematical Science

Typically Offered: Fall, Spring

Typically Offered: Fall, Spring

A study of the calculus of functions of several variables. Concerns the theory and applications of differentiation and integration of functions of several variables, vector fields, line integrals, Green's theorem.This course meets four hours per week.

Prerequisite: MATH 134 or MATH 136 or equivalent

Common Area: Mathematical Science

Typically Offered: Fall, Spring

An introduction to the primary algebraic and analytic structures in abstract mathematics. Emphasis is placed on using the language of sets, equivalence relations and functions, and on developing techniques of proof, including elementary logic and mathematical induction, basic group theory, and limits.

Prerequisite: MATH 134 or MATH 136 or equivalent

Common Area: Mathematical Science

Typically Offered: Fall, Spring

Designed to acquaint students with the basic techniques of linear algebra. Topics include matrices, vector spaces, subspaces, linear transformations, bilinear forms, determinants, eigenvalue theory, and the finite dimensional spectral theorem. Applications and additional topics are included as time permits.

Prerequisite: MATH 243 or permission from Department Chair as it may be possible to take Math 244 before Math 243.

Common Area: Mathematical Science

Typically Offered: Fall, Spring

Centers on some area of geometry other than differential geometry. Possible topics include Euclidean and non-Euclidean geometry, projective geometry, the geometry of transformation groups, and the elementary geometry of algebraic curves.

Typically Offered: Alternate Years

A first course in the differential geometry of curves and surfaces for students who have completed Mathematics 241 and a semester course in linear algebra. Topics include the Frenet-Serret formulas, smooth surfaces in 3-space, fundamental forms, differentiable manifolds, vector fields, connections and a brief introduction to Riemannian geometry.

Introduction to the role of mathematics as a modeling tool, including the construction, interpretation and application of mathematical models. Applications chosen to illustrate various modeling paradigms such as deterministic, probabilistic, discrete and continuous modeling and may include population dynamics, biomedical applications, stock market analysis, and network and traffic flows.

Prerequisite: MATH 241 and MATH 244 or equivalent or permission from Instructor.

Typically Offered: Alternate Years

Linear differential equations are studied basic existence theorems are proved. Separation of variables, Laplace transforms, first- and second-order equation and linear systems, and topics in nonlinear systems are considered. Breadth area: Applied Mathematics/Statistics.

Typically Offered: Alternate Years

The fundamentals of complex analysis. Topics include the complex number system, analytic functions, the Cauchy-Riemann equations, Cauchy's integral theorem, Cauchy's integral formula, Taylor series, Laurent series, the calculus of residues and conformal mapping. Breadth area: Analysis.

Typically Offered: Alternate Years

An in-depth study of the structure of groups, rings and fields. Depending on the instructor, applications to Galois theory, number theory, geometry, topology, physics, etc., are presented.

A continuation of Mathematics 351 exploring advanced topics and applications in modern algebra. Breadth Area: Algebra.

Typically Offered: Alternate Years

Elementary number theory is concerned with properties of numbers (integers, primes, etc.) as well as patterns and relationships among certain sets of numbers. Topics will include divisibility, congruences, special types of primes, the distribution of primes throughout the integers, number-theoretic functions, quadratic residues, and continued fractions. Further study may include the RSA code, a superior encryption algorithm based on elementary number theory, and a discussion of one of the most famous problems in mathematics - Fermat's Last Theorem - conjectured in 1630 yet unsolved until the 1990s. Breadth area: Algebra.

Prerequisite: MATH 243 and 244 or permission of the instructor.

Typically Offered: Alternate Years

A breadth-first introduction to the subject that discusses a representative sampling of combinatorial problems and general techniques for solving them, including a selection of counting techniques, techniques for existence questions, and a variety of examples. Examples may include partitions, graphs and trees, tournaments, graph coloring and chromatic polynomials, magic squares, Latin rectangles and squares, and combinatorial block designs.

Topological ideas are introduced through a treatment of metric space topology. After the study of open, closed, compact and connected spaces with emphasis on their behavior under continuous mappings, selected topics from functional analysis are considered. These include lim sup and lim inf, relation of uniform convergence to differentiation and integration, and the Stone-Weierstrass approximation theorem.

A continuation of Mathematics 361 exploring advanced topics, including an introduction to Lebesgue-Stieltjes integration, Hilbert space and other material from linear space theory. Breadth Area: Analysis.

Typically Offered: Alternate Years

Considers various aspects of topology of surfaces and solids, including orientability, the Euler number, and the fundamental group. One of the goals of the course is the topological classification of surfaces. Breadth area: Geometry/Topology.

Prerequisite: MATH 241, MATH 243 and Prereq or Coreq MATH 244

Typically Offered: Alternate Years

The numerical solution of problems using computers. Considerable time is devoted to selecting the appropriate algorithm for a given problem and analyzing the resulting numerical errors. Includes such topics as error analysis of computer arithmetic, approximation of functions, solution of equations, numerical integration, numerical solution of ordinary differential equations.

Typically Offered: Alternate Years

Provides an understanding of a wide spectrum of phenomena through the use of mathematical ideas, abstractions, and techniques. Topics included are partial differential equations, including the heat and wave equations, Fourier analysis, eigenvalue problems, Green's functions. Breadth area: Applied Mathematics/Statistics.

Prerequisite: MATH 304 or equivalent

Typically Offered: Alternate Years

An introduction to the theory of discrete dynamical systems. Topics include iteration of functions, graphical analysis, periodic points, stable sets, chaos, symbolic dynamics, the dynamics of functions of a complex variable and the Mandelbrot set. The major theorems will be studied along with their proofs and the computer will be used as a research tool to do experiments which motivate and illustrate the theory.

Typically Offered: Alternate Years

Provides an opportunity for individual and group investigation of topics not covered in ordinary course work. Active participation on the part of the students is normally required. Subject matter varies to suit individual students and is often related to the research activity of the professor. Examples of areas of study: Lie groups, functional analysis, complex analysis, probability theory, commutative algebra, applied mathematics, the classical groups, mathematical logic, automata and formal languages, topics in discrete modeling, and qualitative theory of differential equations. A breadth area designation will be made individually for each seminar course by the department chair, in consultation with the faculty member teaching the seminar. Breadth area depends on the subject matter.

Typically Offered: Annually

An independent reading project for upper division students. Normally this is on a topic that is not covered by the regular course offerings. Permission of the instructor and the department chair is required for this course.

Typically Offered: Fall, Spring

A project course for upper division students under the direction of a faculty member. Normally the project will provide an introduction to research on a topic that is not covered by the regular course offerings. Course requirements are to be arranged in consultation with the instructor. Permission of the instructor and the department chair is required for this course.

Typically Offered: Fall, Spring

A large project extending over the course of the fourth year. It can consist of original research or be of an expository nature and is written under the guidance of one or more members of the department. Normally, a student will earn one unit in the spring semester of the fourth year for successful completion of an honors thesis, unless the thesis work is done as part of the student's participation in a departmental seminar. In that case, no extra credit is given above the credit for the seminar itself. For a particularly extensive project, and with the permission of the department chair, a student may earn one unit in each semester of the fourth year for completion of the thesis.

Typically Offered: Annually

A large project extending over the course of the fourth year. It can consist of original research or be of an expository nature and is written under the guidance of one or more members of the department. Normally, a student will earn one unit in the spring semester of the fourth year for successful completion of an honors thesis, unless the thesis work is done as part of the student's participation in a departmental seminar. In that case, no extra credit is given above the credit for the seminar itself. For a particularly extensive project, and with the permission of the department chair, a student may earn one unit in each semester of the fourth year for completion of the thesis.

## MATH 241 - Mathematics

An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections of the course will use the software package MATLAB. Credit will be granted for only one of the following: MATH 241 or MATH 340.

#### Prerequisites

#### Topics

**XI. Vectors, Lines and Planes.**

Cartesian coordinates of space

Vectors

Lines

Planes

Dot and cross product

**XII. Vector-valued Functions**

Vector-valued functions

Tangents

Normals

Curvature

**XIII. Partial Derivatives**

Quadric surfaces

Partial derivatives

Chain rule

Directional derivatives

Gradients

Extreme values

Lagrange multipliers

**XIV. Multiple Integrals**

Double and triple integrals

Change of variable

Volume

Surface area

Moments and centers of gravity

**XV. Calculus of Vector Fields**

Line and surface integrals

Green's theorem

Stokes' theorem

Divergence theorem

## 2020-2021 Undergraduate Catalog

A degree in mathematics is an excellent means of preparation for post-college years, whether a student intends to work in business or industry, teach, or pursue graduate studies. At Cal Lutheran we provide a broad and challenging program designed to develop fundamental skills and to prepare students for lifelong learning. The program features small classes with an emphasis on faculty-student interaction, classroom technology to facilitate learning, computer labs for student exploration and discovery, and a focus on interdisciplinary applications. Faculty mentors assist students in reaching their academic and career goals. Students are challenged to explore the many facets of mathematics and its applications through creative and critical thinking. Departmental space is set aside as a study and resource area for majors. Free tutoring for lower division courses is provided in the Math Lab.

The faculty encourage students to apply their mathematical knowledge by participating in internships, carrying out independent projects, and tutoring in the Math Lab. Students synthesize and extend their mathematical experiences in the senior capstone course. Other opportunities include participating in paid summer research programs across the nation, spending a semester studying mathematics abroad, preparing for and competing in national mathematics-related contests, and preparing posters and presentations for seminars and regional or national conferences.

Employers in the public and private sectors seek generalists with critical thinking skills who are capable of adapting to a wide variety of situations. Graduates in mathematics are prepared in this manner and can work in many career fields. These include computer science, engineering, actuarial science, education, business, finance and the natural sciences. Along with finding excellent employment opportunities, Cal Lutheran math majors have also been accepted for graduate studies at top universities throughout the United States.

Students who wish to register for a mathematics course must meet the necessary prerequisites, as stated in the Schedule of Classes and the Undergraduate Catalog. Students unsure of whether they meet the prerequisites should contact a mathematics faculty member. Courses numbered 400 and above are best taken after or concurrently with a 300-level course.

All Cal Lutheran students are required to meet the Mathematical Reasoning Proficiency under Core 21. Students who meet the proficiency requirement may still need to meet specific mathematics requirements for their majors

## Mathematics (MATH)

MATH 134 exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.

Exam dates: 9/23, 10/21 and 11/2382773 MATH 134 001 Precalc: Elementary Functions 2 TBA 30 0 4 6 MW 0230- 0400p KELL 303 08/23-12/17 Exam dates: 9/23, 10/21 and 11/2382774 MATH 134 002 Precalc: Elementary Functions 2 TBA 30 0 5 5 MW 0330- 0500p KELL 302 08/23-12/17 Exam dates: 9/24, 10/22 and 11/2482775 MATH 134 003 Precalc: Elementary Functions 2 TBA 30 0 9 1 TR 0130- 0300p HIG 110 08/23-12/17 Exam dates: 9/24, 10/22 and 11/2482777 MATH 134 004 Precalc: Elementary Functions 2 TBA 30 0 4 6 TR 0230- 0400p KELL 302 08/23-12/17 Exam dates: 9/24, 10/22 and 11/2482776 MATH 134 005 Precalc: Elementary Functions 2 TBA 30 0 5 5 TR 0315- 0445p BIL 335 08/23-12/17MATH 140 Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.

FQ,FS,H19 79700 MATH 140 001 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 1 9 TBA TBA ONLINE 08/23-12/17 MW 0930- 1020a KUY 209 08/23-12/17 FQ,FS,H19 79701 MATH 140 002 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 3 7 TBA TBA ONLINE 08/23-12/17 MW 1030- 1120a KUY 209 08/23-12/17 FQ,FS,H19 79702 MATH 140 003 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 2 8 TBA TBA ONLINE 08/23-12/17 MW 1130- 1220p KUY 209 08/23-12/17 FQ,FS,H19 79699 MATH 140 004 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 3 7 TBA TBA ONLINE 08/23-12/17 MW 1230- 0120p KUY 209 08/23-12/17 C19,FQ,FS 82859 MATH 140 005 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 0 10 TBA TBA ONLINE 08/23-12/17 MW 0130- 0220p ONLINE 08/23-12/17 FQ,FS,H19 79703 MATH 140 006 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 0 10 TBA TBA ONLINE 08/23-12/17 TR 0830- 0920a KUY 301 08/23-12/17 FQ,FS,H19 81897 MATH 140 007 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 0 10 TBA TBA ONLINE 08/23-12/17 TR 0930- 1020a KUY 301 08/23-12/17 FQ,FS,H19 82217 MATH 140 008 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 1 9 TBA TBA ONLINE 08/23-12/17 TR 1030- 1120a KUY 209 08/23-12/17 FQ,FS,H19 82556 MATH 140 009 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 0 10 TBA TBA ONLINE 08/23-12/17 TR 1130- 1220p KUY 209 08/23-12/17 FQ,FS,H19 82682 MATH 140 010 Precalc:Trig/Analytic Geometry 3 J C Robertson 25 0 0 10 TBA TBA ONLINE 08/23-12/17 TR 1230- 0120p KUY 209 08/23-12/17 FQ,FS,H19,NI 82218 MATH 215 001 Applied Calculus I 4 D Takagi 28 2 0 10 MWF 1230- 0120p ONLINE 08/23-12/17 TR 0930- 1020a KUY 306 08/23-12/17 FQ,FS,H19,NI 81697 MATH 215 002 Applied Calculus I 4 D Takagi 28 2 0 10 MWF 1230- 0120p ONLINE 08/23-12/17 TR 1200- 1250p PHYSCI 217 08/23-12/17 FQ,FS,H19,NI 81698 MATH 215 003 Applied Calculus I 4 D Takagi 26 4 0 10 MWF 1230- 0120p ONLINE 08/23-12/17 WF 0930- 1020a BIL 335 08/23-12/17 FQ,FS,H19,NI 82860 MATH 215 004 Applied Calculus I 4 D Takagi 30 0 1 9 MWF 1230- 0120p ONLINE 08/23-12/17 WF 1130- 1220p PHYSCI 217 08/23-12/17All sections of MATH 241 will have common exams in the evenings. MATH 241 Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.

All sections of MATH 242 will have common exams in the evenings. Dates and times to be advised. Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.

NI 79707 MATH 242 001 Calculus II 4 TBA 25 0 0 10 MWF 0930- 1020a TBA 08/23-12/17 R 1200- 1250p KELL 302 08/23-12/17 NI 79708 MATH 242 002 Calculus II 4 TBA 25 0 0 10 MWF 0930- 1020a TBA 08/23-12/17 R 0130- 0220p KELL 302 08/23-12/17 NI 79709 MATH 242 003 Calculus II 4 F Nasrin 24 0 2 8 MWF 1230- 0120p ART 132 08/23-12/17 T 0830- 0920a KUY 306 08/23-12/17 NI 79710 MATH 242 004 Calculus II 4 F Nasrin 25 0 5 5 MWF 1230- 0120p ART 132 08/23-12/17 T 1200- 1250p KELL 302 08/23-12/17 C19,NI 79711 MATH 242 005 Calculus II 4 TBA 25 0 2 8 TR 0900- 1015a ONLINE 08/23-12/17 W 0930- 1020a ONLINE 08/23-12/17 C19,NI 81694 MATH 242 006 Calculus II 4 TBA 25 0 4 6 TR 0900- 1015a ONLINE 08/23-12/17 W 1230- 0120p ONLINE 08/23-12/17 C19,NI 81902 MATH 242 007 Calculus II 4 TBA 25 0 1 9 TR 1200- 0115p ONLINE 08/23-12/17 F 1030- 1120a ONLINE 08/23-12/17 C19,NI 81905 MATH 242 008 Calculus II 4 TBA 22 3 0 10 TR 1200- 0115p ONLINE 08/23-12/17 F 1230- 0120p ONLINE 08/23-12/17 Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.C19,NI 82222 MATH 243 001 Calculus III 3 TBA 0 0 10 10 MWF 1130- 1220p ONLINE 08/23-12/17 Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.NI 79712 MATH 243 002 Calculus III 3 TBA 30 0 3 7 MWF 0130- 0220p TBA 08/23-12/17 Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.C19,NI 82862 MATH 243 003 Calculus III 3 TBA 30 0 2 8 TR 0900- 1015a ONLINE 08/23-12/17 Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.C19,NI 85714 MATH 243 004 Calculus III 3 TBA 30 0 3 7 TR 1200- 0115p ONLINE 08/23-12/17MATH 244 exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.

MATH 251A is an Honors/Selected Studies course. Students interested in MATH 251A must contact the Mathematics Department to schedule an interview with the Mathematics Department Associate Chair.

MATH 252A is an Honors/Selected Studies course. Students interested in MATH 252A must contact the Mathematics Department to schedule an interview with the Mathematics Department Associate Chair.

Exams must be taken at a proctored UH Test Center (https://www.uhonline.hawaii.edu/testcenters), or other proctored site or service (physical or online) approved by the instructor. See syllabus for details.NI 83815 MATH 252A 001 Accelerated Calculus IIRestriction: Honors Program Approval 4 TBA 2 28 0 10 MWF 1030- 1120a KELL 302 08/23-12/17 W 0930- 1020a KELL 302 08/23-12/17

MATH 253A is an Honors/Selected Studies course. Students interested in MATH 253A must contact the Mathematics Department to schedule an interview with the Mathematics Department Associate Chair.

NOTE: Courses numbered 600 and above are restricted to classified graduate students only. All unclassified students must obtain approval from the department to register.

## Mathematics Majors and Statistics Majors

The Mathematics Department offers four majors. Students may earn a Bachelor of Arts in Mathematics, a Bachelor of Science in Mathematics, a Bachelor of Science in Applied Mathematical Sciences or a Bachelor of Science in Statistics. The choice of degree program depends largely upon the student’s mathematical or statistical objectives and interests in fields other than mathematics. Students with strong interests outside mathematics have options including a Bachelor of Science in Applied Mathematical Sciences, a Bachelor of Arts in Mathematics or a Bachelor of Science in the Mathematical Economics program.

Students in each major complete an introductory year of calculus during their first year, or fulfill this requirement by achieving a high score on the Advanced Placement Test of the College Entrance Examination Board. Students with a strong interest in a career in mathematics or science – and in particular, students planning to continue on to Ph.D. programs in the mathematical sciences – are strongly advised to take courses beyond the minimum requirements for the major. Since the number of courses to be taken in any one department is restricted to 12 for a Bachelor of Arts degree, such students are advised to choose one of the Bachelor of Science majors.

## Featured Alumni

### Hunter Boudreaux

#### Actuarial Assistant I, Protective Life

#### Why did you choose Louisiana Tech University?

Since Ruston is a college town, I enjoyed that both Louisiana Tech and the City of Ruston seemed to care about the students. I also felt that Tech’s College of Engineering and Science helped prepare students to face problems in the real world more so than other programs I considered. Finally, the financial aid and support Louisiana Tech provided made it so that I could go to college for a fraction of the cost had I gone elsewhere.

#### Why did you choose to major in Math?

Growing up, I was always fascinated with math and viewed problem-solving like a game. There’s something exciting about the fact that for any given problem, there are only a handful of solutions, and you’re trying to find those solutions out of an infinite number of possibilities. I wasn’t always sure what I wanted to do with my degree, but I knew that I wouldn’t be happy unless my job involved using math every day.

#### How did Louisiana Tech and the Math Program help you grow as a person and as a professional?

I believe the Math Program taught me how to approach problems both inside and outside of the classroom. I learned that it’s not only important to know how to solve a problem, but if you can’t effectively communicate how you arrived at your answer, how can someone use and trust your work? Additionally, the Math program gave me the confidence that no matter what career path I went down, I would have the quantitative skills needed to succeed.

#### What was your favorite part of being a Tech/Math student?

My favorite part of being a Tech student was being able to see the friends I had made every day. I was heavily involved in the Association of Catholic Tech Students (ACTS), and firmly believe that without the support system and community there, college would have been a lot tougher.

#### What’s the biggest misconception about majoring in math?

I believe the biggest misconception about majoring in math is the lack of opportunities you’ll have available to you. I started my career as a financial analyst for a healthcare company and have since transitioned to being an actuary for a life insurance company. No matter the industry, there’s always a need for problem solvers who can effectively communicate their work. It’s important to see what’s out there and to network with whoever you can.

#### What’s the most important piece of advice you would give incoming or current Tech/Math students?

The most important piece of advice I’d give incoming Tech students is to try anything and everything that you can. Find out what you like, what you don’t like, and don’t be afraid to put yourself out there. College will be an important time to learn and study, but don’t forget to take breaks and have fun along the way.

## Department of Mathematics

**511 - Probability (3)** Probability and independence discrete and continuous random variables joint, marginal, and conditional densities, moment generating functions laws of large numbers binomial, Poisson, gamma, univariate, and bivariate normal distributions.**Prerequisites:** C or higher or concurrent enrollment in MATH 241 or consent of the Undergraduate Director

**514 - Financial Mathematics I (3)** Probability spaces. Random variables. Mean and variance. Geometric Brownian Motion and stock price dynamics. Interest rates and present value analysis. Pricing via arbitrage arguments. Options pricing and the Black-Scholes formula.**Prerequisites:** C or higher or concurrent enrollment in MATH 241 or consent of the Undergraduate Director

**515 - Financial Mathematics II (3)** Convex sets. Separating Hyperplane Theorem. Fundamental Theorem of Asset Pricing. Risk and expected return. Minimum variance portfolios. Capital Asset Pricing Model. Martingales and options pricing. Optimization models and dynamic programming.**Prerequisites:** C or better in MATH 514 or STAT 522 or consent of the Undergraduate Director

**520 - Ordinary Differential Equations (3)** Differential equations of the first order, linear systems of ordinary differential equations, elementary qualitative properties of nonlinear systems.**Prerequisites:** C or better in MATH 344 or 544 or consent of the Undergraduate Director

**521 - Boundary Value Problems and Partial Differential Equations (3)** Laplace transforms, two-point boundary value problems and Green’s functions, boundary value problems in partial differential equations, eigenfunction expansions and separation of variables, transform methods for solving PDE’s, Green’s functions for PDE’s, and the method of characteristics.**Prerequisites:** C or better in MATH 520 or MATH 241 and 242 or consent of the Undergraduate Director

**522 - Wavelets (3)** Basic principles and methods of Fourier transforms, wavelets, and multiresolution analysis applications to differential equations, data compression, and signal and image processing development of numerical algorithms. Computer implementation.**Prerequisites:** C or better in MATH 344 or 544 or consent of the Undergraduate Director

**523 - Mathematical Modeling of Population Biology (3)** Applications of differential and difference equations and linear algebra modeling the dynamics of populations, with emphasis on stability and oscillation. Critical analysis of current publications with computer simulation of models.**Prerequisites:** C or better in MATH 142, BIOL 301, or MSCI 311 recommended

**524 - Nonlinear Optimization (3)** Descent methods, conjugate direction methods, and Quasi-Newton algorithms for unconstrained optimization globally convergent hybrid algorithm primal, penalty, and barrier methods for constrained optimization. Computer implementation of algorithms.**Prerequisites:** C or better in MATH 344 or 544 or consent of the Undergraduate Director

**525 - Mathematical Game Theory (3)** Two-person zero-sum games, minimax theorem, utility theory, n-person games, market games, stability.**Prerequisites:** C or better in MATH 544 or in both MATH 300 and 344, or consent of the Undergraduate Director

**526 - Numerical Linear Algebra (4)** Matrix algebra, Gauss elimination, iterative methods overdetermined systems and least squares eigenvalues, eigenvectors numerical software. Computer implementation. Credit may not be received for both MATH 526 and MATH 544.**Prerequisites:** Concurrent enrollment in or C or better in MATH 142 or consent of the Undergraduate Director

**527 - Numerical Analysis (3)** Interpolation and approximation of functions solution of algebraic equations numerical differentiation and integration numerical solutions of ordinary differential equations and boundary value problems computer implementation of algorithms.**Prerequisites:** C or better MATH 520 or in both MATH 242 and 344, or consent of the Undergraduate Director

**531 - Foundations of Geometry (3)** The study of geometry as a logical system based upon postulates and undefined terms. The fundamental concepts and relations of Euclidean geometry developed rigorously on the basis of a set of postulates. Some topics from non-Euclidean geometry.

Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director

**532 - Modern Geometry (3)** Projective geometry, theorem of Desargues, conics, transformation theory, affine geometry, Euclidean geometry, non-Euclidean geometries, and topology.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**533 - Elementary Geometric Topology (3)** Topology of the line, plane, and space, Jordan curve theorem, Brouwer fixed point theorem, Euler characteristic of polyhedra, orientable and non-orientable surfaces, classification of surfaces, network topology.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**534 - Elements of General Topology (3)** Elementary properties of sets, functions, spaces, maps, separation axioms, compactness, completeness, convergence, connectedness, path connectedness, embedding and extension theorems, metric spaces, and compactification.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**540 - Modern Applied Algebra (3)** Finite structures useful in applied areas. Binary relations, Boolean algebras, applications to optimization, and realization of finite state machines.**Prerequisites:** MATH 241

**541 - Algebraic Coding Theory (3)** Error-correcting codes, polynomial rings, cyclic codes, finite fields, BCH codes**Prerequisites:** C or better in MATH 544 or in both MATH 300 and 344 or consent of the Undergraduate Director

**544 - Linear Algebra (3)** Vectors, vector spaces, and subspaces geometry of finite dimensional Euclidean space linear transformations eigenvalues on theoretical concepts, logic, and methods.**Prerequisites:** C or better in MATH 300, or consent of the Undergraduate Director

**544L - Linear Algebra Lab (1)** Computer-based applications of linear algebra for mathematics students. Topics include numerical analysis of matrices, direct and indirect methods for solving linear systems, and least squares method (regression). Typical applications include theoretical and practical issues related to discrete Markov’s processes, image compression, and linear programming.**Prerequisites:** Prereq or coreq: C or better or concurrent enrollment in MATH 544.

**546 - Algebraic Structures I (3)** Permutation groups abstract groups introduction to algebraic structures through study of subgroups, quotient groups, homomorphisms, isomorphisms, direct product decompositions introduction to rings and fields.

**Prerequisites:**C or better in MATH 544 or consent of the Undergraduate Director

**547 - Algebraic Structures II (3)** Rings, ideals, polynomial rings, unique factorization domains structure of finite groups topics from: fields, field extensions, Euclidean constructions, modules over principal ideal domains (canonical forms).**Prerequisites**: C or higher in MATH 546 or consent of the Undergraduate Director

**548 - Geometry, Algebra, and Algorithms (3)** Polynomials and affine space, Groebner bases, elimination theory, varieties, and computer algebra systems.**Prerequisites:** Math 300 and Math 544 or consent of the Undergraduate Director.

**550 - Vector Analysis (3)** Vector fields, line and path integrals, orientation and parametrization of lines and surfaces, change of variables and Jacobians, oriented surface integrals, theorems of Green, Gauss, and Stokes introduction to tensor analysis.**Prerequisites:** C or higher in MATH 241 or consent of the Undergraduate Director

**551 - Introduction to Differential Geometry (3)** Parameterized curves, regular curves and surfaces, change of parameters, tangent planes, the differential of a map, the Gauss map, first and second fundamental forms, vector fields, geodesics, and the exponential map.

Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director

**552 - Applied Complex Variables (3)** Complex integration, calculus of residues, conformal mapping, Taylor and Laurent Series expansions, applications.**Prerequisites:** C or better in MATH 241 or consent of the Undergraduate Director

**554 - Analysis I (3)** Least upper bound axiom, the real numbers, compactness, sequences, continuity, uniform continuity, differentiation, Riemann integral and fundamental theorem of calculus.**Prerequisites:** C or better in MATH 300 and either at least one of 511, 520, 534, 550, or 552, or consent of the Undergraduate Director

**555 - Analysis II (3)** Riemann-Stieltjes integral, infinite series, sequences and series of functions, uniform convergence, Weierstrass approximation theorem, selected topics from Fourier series or Lebesgue integration.**Prerequisites:** C or better in MATH 554 or consent of the Undergraduate Director

**561 - Introduction to Mathematical Logic (3)** Syntax and semantics of formal languages sentential logic, proofs in first order logic Godel’s completeness theorem compactness theorem and applications cardinals and ordinals the Lowenheim-Skolem-Tarski theorem Beth’s definability theorem effectively computable functions Godel’s incompleteness theorem undecidable theories.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**562 - Theory of Computation (3)** Basic theoretical principles of computing as modeled by formal languages and automata computability and computational complexity.**Prerequisites:** C or better in CSCE 350 or MATH 344 or 544 or 574 or consent of the Undergraduate Director

**570 - Discrete Optimization (3)** Discrete mathematical models. Applications to such problems as resource allocation and transportation. Topics include linear programming, integer programming, network analysis, and dynamic programming.**Prerequisites:** C or better in MATH 344 or 544, or consent of the Undergraduate Director

**574 - Discrete Mathematics I (3)** Mathematical models mathematical reasoning enumeration induction and recursion tree structures networks and graphs analysis of algorithms.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**575 - Discrete Mathematics II (3)** A continuation of MATH 574. Inversion formulas Polya counting combinatorial designs minimax theorems probabilistic methods Ramsey theory other topics.**Prerequisites:** C or better in MATH 574 or consent of the Undergraduate Director

**576 - Combinatorial Game Theory (3)** Winning in certain combinatorial games such as Nim, Hackenbush, and Domineering. Equalities and inequalities among games, Sprague-Grundy theory of impartial games, games which are numbers.**Prerequisites:** C or better in MATH 344, 544, or 574, or consent of the Undergraduate Director

**580 - Elementary Number Theory (3)** Divisibility, primes, congruences, quadratic residues, numerical functions. Diophantine equations.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**587 - Introduction to Cryptography (3)** Design of secret codes for secure communication, including encryption and integrity verification: ciphers, cryptographic hashing, and public key cryptosystems such as RSA. Mathematical principles underlying encryption. Code-breaking techniques. Cryptographic protocols.**Prerequisites**: C or better in CSCE 145 or in MATH 241, and in either CSCE 355 or MATH 574, or consent of the Undergraduate Director

**590 - Undergraduate Seminar (1-3)** A review of literature in specific subject areas involving student presentations. Content varies and will be announced in the Master Schedule of Classes by suffix and title. Pass-fail grading. For undergraduate credit only.**Prerequisites:** consent of instructor

**599 - Topics in Mathematics (1-3)** Recent developments in pure and applied mathematics selected to meet current faculty and student interest.**602 - An Inductive Approach to Geometry (3)** This course is designed for middle-level pre-service mathematics teachers. This course covers geometric reasoning, Euclidean geometry, congruence, area, volume, similarity, symmetry, vectors, and transformations. Dynamic software will be utilized to explore geometry concepts.

**Prerequisites:**C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director

**603 - Inquiry Approach to Algebra (3)** This course introduces basic concepts in number theory and modern algebra that provide the foundation for middle level arithmetic and algebra. Topics include: algebraic reasoning, patterns, inductive reasoning, deductive reasoning, arithmetic and algebra of integers, algebraic systems, algebraic modeling, and axiomatic mathematics. This course cannot be used for credit towards a major in mathematics.**Prerequisites:** C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director

**650 - AP Calculus for Teachers (3)** A thorough study of the topics to be presented in AP calculus, including limits of functions, differentiation, integration, infinite series, and applications. (Not intended for degree programs in mathematics.)**Prerequisites**: current secondary high school teacher certification in mathematics and a C or better in at least 6 hours of calculus, or consent of the Undergraduate Director

**701I — Foundations of Algebra I. (3)** An introduction to algebraic structures group theory including subgroups, quotient groups, homomorphisms, isomorphisms, decomposition introduction to rings and fields.**Prerequisites**: none

**702I — Foundations of Algebra II. (3)** Theory of rings including ideals, polynomial rings, and unique factorization domains structure of finite groups fields modules.**Prerequisites:** MATH 701-I or equivalent

**703I — Foundations of Analysis I. (3)** The real numbers and least upper bound axiom sequences and limits of sequences infinite series continuity differentiation the Riemann integral.**Prerequisites**: MATH 241 or equivalent**704I — Foundations of Analysis II. (3)** Sequences and series of functions power series, uniform convergence interchange of limits limits and continuity in several variables.

**Prerequisites**: MATH 703-I or equivalent

**712I — Probability and Statistics. (3)** This course will include a study of permutations and combinations probability and its application to statistical inferences elementary descriptive statistics of a sample of measurements the binomial, Poisson, and normal distributions correlation and regression.**Prerequisites**:

736I — Modern Geometry. (3) Synthetic and analytic projective geometry, homothetic transformations, Euclidean geometry, non-Euclidean geometries, and topology.**Prerequisites**: MATH 241 or equivalent

752I — Complex Variables. (3) Properties of analytic functions, complex integration, calculus of residues, Taylor and Laurent series expansions, conformal mappings.**Prerequisites**: MATH 241 or equivalent

780I — Theory of Numbers. (3) Elementary properties of integers, Diophantine equations, prime numbers, arithmetic functions, congruences, and the quadratic reciprocity law.**Prerequisites**: MATH 241 or equivalent