Master of Science (M.S.) Major in Applied Mathematics
Application Requirements
The items listed below are required for admission consideration for applicable semesters of entry during the 20172018 academic year. Submission instructions, additional details, and changes to admission requirements for semesters other than the 20172018 academic year can be found on the program’s web page. International students should review the International Admission Documents section of the catalog for additional requirements.
 completed online ApplyTexas application
 $40 nonrefundable application fee
 $50 nonrefundable international evaluation fee (if applicable)
 baccalaureate degree in mathematics or a related field from a regionally accredited university
 official transcripts required from each institution where course credit was granted
 minimum 2.75 GPA in your last 60 hours of undergraduate course work (plus any completed graduate courses)
 background course work
 official GRE scores required with a preferred minimum of 300 (verbal and quantitative sections combined)

The GRE may be waived if you hold a master's or doctoral degree from a regionally accredited U.S. institution. If you hold a master's or doctoral degree (or the equivalent thereof) from an accredited international institution, the GRE may be waived on an individual basis.

TOEFL or IELTS Scores
Nonnative English speakers who do not qualify for an English proficiency waiver:
 official TOEFL iBT scores required with a 78 overall
 official IELTS (academic) scores required with a 6.5 overall and
 minimum individual module scores of 6.0
This program does not offer admission if the scores above are not met.
Degree Requirements
The Master of Science (M.S.) major in Applied Mathematics consists of 24 hours of mathematics plus a thesis.
Course Requirements
Code  Title  Hours 

MATH 5373  Theory of Functions of Real Variables  3 
MATH 5355  Applied and Algorithmic Graph Theory  3 
MATH 5345  Regression Analysis  3 
Support Electives  
Choose 9 hours from the following:  9  
Partial Differential Equations  
Functions of a Complex Variable  
Scientific Computation  
Mathematical Modeling  
Design and Analysis of Experiments  
Analysis of Variance  
Electives  
Choose 6 hours from the following:  6  
Advanced Course in Probability and Statistics  
Modern Algebra  
Field Theory  
General Topology  
Studies in Applied Mathematics  
Combinatorics  
Applied Discrete Mathematics  
Thesis  
Choose a minimum 6 hours from the following:  6  
Thesis  
Thesis  
Thesis  
Thesis  
Thesis  
Thesis  
Total Hours  30 
If a student elects to follow the thesis option for the degree or if the degree requires a thesis, a committee to direct the written thesis will be established. The thesis must demonstrate the student’s capability for research and independent thought. Preparation of the thesis must be in conformity with the Graduate College Guide to Preparing and Submitting a Thesis or Dissertation. The thesis handbook may be accessed at http://www.gradcollege.txstate.edu/docs/Thesis_Diss_Guide.pdf.
Thesis Proposal
The student must submit an official Master's Thesis Proposal form and proposal to his or her thesis committee. Thesis proposals vary by department and discipline. Please see your department for proposal guidelines and requirements. The required thesis proposal form may be obtained from The Graduate College at http://www.gradcollege.txstate.edu/gcforms.html. After signing the form and obtaining committee members’ signatures, graduate advisor’s signature (if required by the program), and the department chair’s signature, the student must submit the thesis proposal form with one copy of the proposal attached to the dean of The Graduate College for approval before proceeding with research on the thesis. If the thesis research involves human subjects, the student must obtain exemption or approval from the Texas State Institutional Review Board prior to submitting the proposal form to The Graduate College. If the thesis research involves vertebrate animals, the proposal form must include the Texas State IACUC approval code. It is recommended the thesis proposal form be submitted to the dean of The Graduate College by the end of the student’s enrollment in 5399A.
Thesis Committee
The thesis committee must be composed of a minimum of three approved graduate faculty members.
Thesis Enrollment and Credit
The completion of a minimum of six hours of thesis enrollment is required. Enrollment for the thesis will be in course number 5399A for a student’s initial thesis enrollment and a thesis B course for each subsequent thesis enrollment in the field in which the subject matter of the thesis falls, e.g., PS 5399A and PS 5399B. Preliminary discussions regarding the selection of a topic and assignment to a research supervisor will not require enrollment for the thesis course.
A student will be required to enroll in and pay the fee for at least one hour of the thesis course during any term in which the student will receive thesis supervision or guidance and/or in which the student is using university resources. Failure to register for the thesis course during a term in which supervision is received may result in postponement of graduation. After initial enrollment in 5399A, the student will continue to enroll in a thesis B course as long as it takes to complete the thesis. In the rare case when a student has not previously enrolled in thesis and plans to work on and complete the thesis in one term, the student will enroll in both 5399A and 5399B. The only grades assigned for thesis courses are PR (progress), CR (credit), W (withdrew), and F (failing). If acceptable progress is not being made in a thesis course, the instructor may issue a grade of F. If the student is making acceptable progress, a grade of PR is assigned until the thesis is completed. The minimum number of hours of thesis credit (“CR”) will be awarded only after the thesis is filed in the Alkek Library and the librarian has electronically returned the thesis card to the office of The Graduate College.
A student who has selected the thesis option must be registered for the thesis course during the term or Summer I (during summer the thesis course runs ten weeks for both sessions) in which the degree will be conferred.
Fee Reduction
A master’s degree candidate for graduation may be eligible for a onetime fee reduction under V.T.C.A. Education Code, Section 54.054. Please refer to the section titled Fee Reduction in the Additional Fees and Expenses chapter of this catalog for more information.
Thesis Deadlines and Approval Process
Thesis deadlines are posted at the following web page: http://www.gradcollege.txstate.edu/ThesDiss_Info/TD_Deadlines.html. The completed thesis must be submitted to the chair of the thesis committee no later than 41 days before the date of the commencement at which the degree is to be conferred.
The following must be submitted to the office of The Graduate College no later than 24 days, not counting weekends or holidays, before the date of commencement at which the degree is to be conferred (see The Graduate College webpage for specific deadlines):
 The Thesis/Dissertation Committee Approval form bearing original signatures of the student and all committee members.
 One (1) copy of the thesis in final form, approved by all committee members, on standard paper (Hardcopy Submission Option) or PDF of the thesis in final form, approved by all committee members, uploaded in the online Vireo submission system (Vireo Online Submission Option).
After the dean of The Graduate College approves the thesis, the process is as follows:
 For the Vireo Online Submission Option:
 No copies are required to be submitted to the Alkek Library. However, Alkek will bind copies submitted that the student wants bound for personal use. Personal copies are not required to be printed on archival quality paper. The student will take the personal copies to the Alkek Library and pay the binding fee for personal copies.
Master's level courses in Mathematics: MATH, MTE
Courses Offered
Mathematics (MATH)
MATH 5111. Graduate Assistant Training.
This course is concerned with techniques used in the teaching of mathematics. This course is required as a condition of employment for graduate teaching and instructional assistants. This course does not earn graduate degree credit. Repeatable with different emphasis. Graded on a credit (CR), nocredit (F) basis.
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Course Attribute(s): Graduate AssistantshipExclude from Graduate GPA
Grade Mode: Leveling/Assistantships
MATH 5199B. Thesis.
This course represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding. Graded on a credit (CR), progress (PR), nocredit (F) basis.
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Grade Mode: Credit/No Credit
MATH 5299B. Thesis.
This course represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding. Graded on a credit (CR), progress (PR), nocredit (F) basis.
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Grade Mode: Credit/No Credit
MATH 5301. Partial Differential Equations.
Theory and application of partial differential equations; derivation of the differential equation; use of vector and Tensor methods; equations of the
first order; wave equations; vibrations and normal functions; Fourier series and integral; Cauchy’s methods, initial data; methods of Green; potentials; boundary problems; methods of RiemannVolterra; characteristics. Prerequisites: MATH 3323 and consent of the instructor.
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Grade Mode: Standard Letter
MATH 5303. History of Mathematics.
A study of the development of mathematics and of the accomplishments of men and women who contributed to its progress. Cannot be used on a degree plan
for M.S. degree. Prerequisite: A grade of at least C in MATH 2472.
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Grade Mode: Standard Letter
MATH 5304. Topics in Mathematics for the Secondary Teacher.
A study of the current trends and topics found in the secondary school mathematics curriculum with the goal of improving the mathematical background of the secondary teacher. Course content will be flexible and topics will be
selected on the basis of student needs and interests. Cannot be used on degree plan for M.S. degree. Prerequisite: A grade of C in MATH 2472.
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MATH 5305. Advanced Course in Probability and Statistics.
Advanced topics in probability and statistics. May be repeated once with different emphasis for additional credit. Prerequisite: MATH 3305.
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MATH 5306. Ring Theory.
Prerequisite: A grade of at least a “C” in MATH 4307 or a grade of at least a “B” in MATH 5384.
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Grade Mode: Standard Letter
MATH 5307. Modern Algebra.
Topics in modern algebra. Material will be adapted to the needs of the class. Prerequisite: A grade of at least a C in MATH 4307 or a grade of at least a B in
MATH 5384.
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Grade Mode: Standard Letter
MATH 5311. Foundations of Differential Equations.
A critical study of the foundations of derivation equations, operator spaces, and such basic topics. Recent developments in this field will be investigated and independent investigation will be encouraged. Prerequisite: A grade of at least a C in MATH 3373 and either 3380 or 5382.
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Grade Mode: Standard Letter
MATH 5312. Functions of a Complex Variable.
Modern developments in the field of a complex variable. Prerequisite: A grade of at least a C in MATH 3373; either 3380 or 5382; and 4315 or departmental approval.
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Grade Mode: Standard Letter
MATH 5313. Field Theory.
Topics in field theory, separable extensions, and Galois Theory. Prerequisite: A grade of at least a C in MATH 4307 or a grade of at least a B in MATH 5384.
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Grade Mode: Standard Letter
MATH 5314. Number Theory.
Topics in algebra selected from quadratic forms, elementary number theory, algebraic or analytic number theory, with material adapted to the needs of the class. Prerequisite: A grade of at least a C in MATH 4307 or a grade of at least a B in MATH 5384.
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Grade Mode: Standard Letter
MATH 5317. Problems in Advanced Mathematics.
Open to graduate students on an individual basis by arrangement with the mathematics department. A considerable degree of mathematical maturity is required. May be repeated with different emphasis. This course does not count toward any degree in the Department of Mathematics.
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Course Attribute(s): Exclude from Graduate GPALeveling
Grade Mode: Leveling/Assistantships
MATH 5319. The Theory of Integration.
A course in the theory of integration with special emphasis on the Lebesgue integrals. A course in the theory of real variables, with a knowledge of point
set theory, is desirable as a background for this course. A considerable amount of mathematical maturity is required. Prerequisite: A grade of at least a C in MATH 4315 or departmental approval.
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Grade Mode: Standard Letter
MATH 5329. General Topology.
Pointset topology with an emphasis on general topological spaces; separation axioms, connectivity, the metrization theorem, and the CW complexes. Prerequisite: A grade of at least a C in MATH 4330 or departmental approval.
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Grade Mode: Standard Letter
MATH 5331. Metric Spaces.
Pointset topology with an emphasis on metric spaces and compactness but including a brief introduction to general topological spaces. Prerequisite: A grade of at least a C in MATH 4330 or departmental approval.
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Grade Mode: Standard Letter
MATH 5336. Studies in Applied Mathematics.
Topics selected from optimization and control theory, numerical analysis, calculus of variations, boundary value problems, special functions, or tensor analysis. May be repeated with different emphasis for additional credit. Prerequisites: Six hours of advanced mathematics pertinent to topic and consent of the instructor.
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Grade Mode: Standard Letter
MATH 5340. Scientific Computation.
This course will involve the analysis of algorithms from science and mathematics, and the implementation of these algorithms using a computer algebra system.
Symbolic numerical and graphical techniques will be studied. Applications will be drawn from science, engineering, and mathematics. Prerequisite: MATH 3323 or consent of instructor.
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Course Attribute(s): Lab Required
Grade Mode: Standard Letter
MATH 5345. Regression Analysis.
This course introduces formulation and statistical methodologies for simple and multiple regression, assessment of model fit, model design, and criteria
for selection of optimal regression models. Students will develop skills with the use of statistical packages and the writing of reports analyzing a variety of realworld data. Prerequisite: MATH 2472.
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Grade Mode: Standard Letter
MATH 5350. Combinatorics.
This course, covers permutations, combinations, Stirling numbers, chromatic numbers, Ramsey numbers, generating functions, Polya theory, Latin squares and
random block design. Prerequisite: MATH 3398 or consent of instructor.
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Grade Mode: Standard Letter
MATH 5355. Applied and Algorithmic Graph Theory.
This course is designed to emphasize the close tie between the theoretical and algorithmic aspects. The topics may include basic concepts such as connectivity, trees, planarity, coloring of graphs, matchings, and networks. It also covers many
algorithms such as Maxflow Mincut algorithm, maximum matching algorithm, and optimization algorithms for facility location problems in networks. Prerequisite: MATH 5388 or MATH 3398.
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Grade Mode: Standard Letter
MATH 5358. Applied Discrete Mathematics.
Boolean algebra, counting techniques, discrete probability, graph theory, and related discrete mathematical structures that are commonly encountered in
computer science. Prerequisite: A grade of at least C in MATH 2472.
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Grade Mode: Standard Letter
MATH 5360. Mathematical Modeling.
This course introduces the process and techniques of mathematical modeling. It covers a variety of application areas from the natural sciences. Emphasis is
placed on deterministic systems, stochastic models, and diffusion. Prerequisite: MATH 3373, MATH 3323, and MATH 5301, or consent of instructor.
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Grade Mode: Standard Letter
MATH 5373. Theory of Functions of Real Variables.
This course will discuss those topics that will enable the student to obtain a better grasp of the fundamental concepts of the calculus of real variables and the more recent developments of this analysis. Prerequisite: A grade of at least a C in
MATH 4315 or departmental approval.
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Grade Mode: Standard Letter
MATH 5374. Numerical Linear Algebra.
This course introduces tools that mathematical scientists use with vectors and matrices. Applications include least squares and eigenvalue problems, and systems of equations from applied mathematics. The stability of algorithms to perturbations are considered. Theory is balanced with numerically implementing algorithms, in particular for iterative methods for large, sparse systems. Prerequisite: MATH 3377 with a C or higher.
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Grade Mode: Standard Letter
MATH 5376A. Design and Analysis of Experiments.
This course introduces fundamental concepts in the design of experiments, justification of linear models, randomization and principles of blocking. It also discusses the construction and analysis of basic designs including fractional
replication, composite designs, factorial designs, and incomplete block designs. Prerequisite: Approval of instructor.
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Course Attribute(s): Topics
Grade Mode: Standard Letter
MATH 5376B. Analysis of Variance.
This course introduces basic methods, oneway, twoway ANOVA procedures, and multifactor ANOVA designs. Prerequisite: Approval of instructor.
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Course Attribute(s): Topics
Grade Mode: Standard Letter
MATH 5381. Foundations of Set Theory.
A formal study of the theory of sets, relations, functions, finite and infinite sets, set operations and other selected topics. This course will also train the student in the understanding of mathematical logic and the writing of proofs. Prerequisite: A grade of at least C in MATH 2472.
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MATH 5382. Foundation of Real Analysis.
A course covering the foundations of mathematical analysis. Topics include: real numbers, sequences, series, and limits and continuity of functions.
Prerequisite: MATH 5381.
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Grade Mode: Standard Letter
MATH 5384. Geometric Approach to Abstract Algebra.
Definitions and elementary properties of groups, rings, integral domains, fields and vector spaces with great emphasis on the rings of integers, rational numbers, complex numbers, polynomials, and the interplay between algebra and geometry. Prerequisite: MATH 5381.
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Grade Mode: Standard Letter
MATH 5386. Knots and Surfaces, An Introduction to LowDimensional Topology.
Knot polynomials and other knot invariants. The topological classification of surfaces and topological invariants of surfaces. Prerequisite: A grade of at least C in MATH 2472.
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Grade Mode: Standard Letter
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MATH 5388. Discrete Mathematics.
This course covers topics from: basic and advanced techniques of counting, recurrence relations, discrete probability and statistics, and applications of graph
theory. Prerequisites: A grade of at least C in MATH 2472.
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Grade Mode: Standard Letter
MATH 5390. Statistics.
This course will cover not only some of the basic statistical ideas and techniques but also the mathematical and probabilistic underpinnings of these techniques with an emphasis on simulations and modeling. The planning, conducting, analysis, and reporting of experimental data will also be covered. Prerequisite: A grade of at least C in MATH 2472.
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Grade Mode: Standard Letter
MATH 5392. Survey of Geometries.
A study of topics in geometry including geometrical transformations, the geometry fractals, projective geometry, Euclidean geometry, and nonEuclidean
geometry. Prerequisite: A grade of at least C in MATH 2472.
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MATH 5393. Numerical Optimization.
This course focuses on optimization methods for a broad range of applications, such as engineering and applied sciences. Subjects are the basic theory of optimization, numerical algorithms to locate points satisfying optimality conditions and to analyze the convergence properties. Prerequisites: MATH 2472, MATH 3377 and MATH 3383, with grades of “C” or higher.
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MATH 5399A. Thesis.
This course represents a student’s initial thesis enrollment. No thesis credit is awarded until student has completed the thesis in Mathematics 5399B. Graded on a credit (CR), progress (PR), nocredit (F) basis.
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Grade Mode: Credit/No Credit
MATH 5399B. Thesis.
This course represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding. Graded on a credit (CR), progress (PR), nocredit (F) basis.
Read More [+] about Thesis
Grade Mode: Credit/No Credit
MATH 5599B. Thesis.
This course represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding. Graded on a credit (CR), progress (PR), nocredit (F) basis.
Read More [+] about Thesis
Grade Mode: Credit/No Credit
MATH 5999B. Thesis.
This course represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding. Graded on a credit (CR), progress (PR), nocredit (F) basis.
Read More [+] about Thesis
Grade Mode: Credit/No Credit
Mathematics for Teacher Education (MTE)
MTE 5301E. Visual Models for Middle School Mathematics.
This course uses visual models to motivate understanding of the fundamental concepts underlying middle school mathematics. Pedagogical techniques to engage middle school students will also be addressed including inquirybased
instructional methods utilizing these visual models.
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Course Attribute(s): Topics
Grade Mode: Standard Letter
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MTE 5301F. Implementing New Mathematics Curriculum.
In this course we will investigate the keys to successfully implementing new curriculum. Two main aspects considered are: 1) the mathematical content knowledge required for a new curriculum and 2) how to build a community of
practice which provides support during the implementation process.
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Course Attribute(s): Topics
Grade Mode: Standard Letter
MTE 5301G. Mathematics for Teaching.
A study of the current trends and topics found in the secondary school mathematics curriculum taught from an advance perspective. Course context will be flexible and topics will be selected on the basis of student needs and interests.
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Course Attribute(s): Topics
Grade Mode: Standard Letter
MTE 5302A. Quantitative Reasoning.
This course covers current pedagogy, curriculum, and methods related specifically to the teaching of middle school mathematics. Some of the topics explored are curriculum theory, instructional theory, learning theory, problem solving, national and state standards and assessment, discovery learning, assessment methods, manipulative, and technology in the classroom.
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Course Attribute(s): Topics
Grade Mode: Standard Letter
MTE 5311. Quantitative Reasoning.
This course will focus on numerical reasoning and problem solving with particular attention being placed on strategies for solving problems, methods for mental computation and computational estimation, and algorithmic processes being taught in a studentcentered atmosphere where teachers are free to take risks.
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MTE 5313. Geometry and Measurement.
This course will focus on using spatial reasoning to investigate the concepts of direction, orientation, shape and structure; using mathematical reasoning
to develop and prove geometric relationships; using logical reasoning and proof in relation to the axiomatic structure of geometry; using measurement of geometry concepts to solve realworld problems. 5315 Algebraic Reasoning. (30) This course will focus on using algebraic reasoning to.
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MTE 5315. Algebraic Reasoning.
This course will focus on using algebraic reasoning to investigate patterns, make generalizations, formulate mathematical models, and make predications;
using properties, graphs, and applications of relations and function to analyze, model and solve problems; and making connections among geometric, graphic, numeric and symbolic representation of functions and relations.
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MTE 5317. Math Modeling.
This course will focus on modeling problems, applying appropriate mathematical analysis and drawing conclusions from the analysis; solving problems recursively, using linear and nonlinear functions and using geometry and discrete mathematics to solve problems in Science, Music, and Art. Prerequisite: MTE 5315.
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Grade Mode: Standard Letter
MTE 5319. Concepts of Calculus.
A first course in differential and integral calculus. The student will explore the slope of secant lines, average velocity, limit, instantaneous velocity, derivative,
slope of a curve at a point, area under a graph, integrals, fundamental theorem of calculus, and applications. Prerequisite: MTE 5317 or consent of department chair.
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Grade Mode: Standard Letter
MTE 5321. Probability and Statistics.
This course will deal with using graphical and numerical techniques to explore date, characterize patterns, and describe departures from patterns;
designing experiments to solve problems; understanding the theory of probability and its relationship to sampling and statistical inference and its use in making and evaluating predication. Prerequisite: MTE 5315.
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Grade Mode: Standard Letter
MTE 5323. Logic and Foundations of Mathematics.
This course will consist of an introduction to fundamental mathematical structures and techniques of proof. Topics will include: logic, set theory, number theory, relations, and functions. Emphasis will be placed on communication
about mathematics and construction of wellreasoned explanations. Prerequisite: MTE 5313 and MTE 5319.
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