# MATH-MATHEMATICS

The basic skills requirement in mathematics may be met by earning a grade of C or higher in both MATH 111 and MATH 112, or in any lower-division mathematics course numbered 120 or above. For other options, see Basic Academic Skills in the General Information chapter.

A student may not receive credit for a lower-division mathematics course if it serves as a prerequisite to a lower-division math course that the student had previously passed with a grade of C or better.

NOTE: Students without an adequate placement score to enroll in MATH 111, MATH 120 or MATH 210G can gain admission to the course by earning a C or better in CCDM 114N at an NMSU branch campus. Students wishing to enroll in MATH 121, 142G, 180, 191, 230, 235, 279, 280, or STAT 251 must satisfy one of the following: (a) have passed the stated prerequisite course with a C or better, or (b) have earned an adequate score on the Mathematics Placement Examination, the results of which will be made available to the students advisor. The Mathematics Placement Examination (MPE) is given daily in Walden Hall when school is in session and during new student programs. A student who has not satisfied one of these requirements before registering may enroll temporarily in UNIV 000, then drop/add to an appropriate course at the beginning of the semester after taking the MPE and being advised.

- MATH 101. General Supplemental Instruction I - 1 cr.
- Collaborative workshop for students enrolled in Intermediate Algebra. Corequisite: MATH 120. May be repeated for a maximum of 2 credits. Graded S/U.

- MATH 102. General Supplemental Instruction II - 1 cr.
- Collaborative workshop for students enrolled in College Algebra. Corequisite: MATH 121G. May be repeated for a maximum of 2 credits. Graded S/U.

- MATH 107. Topics in Mathematics - 1-3 cr.
- Topics to be announced in the Schedule of Classes. Maximum of 3 credits per semester. Total credit not to exceed 6 credits. Prerequisite: consent of instructor. Community Colleges only.

- MATH 111. Fundamentals of Elementary Mathematics I - 3 cr.
- Numbers and the four operations of arithmetic. Understanding and comparing multiple representations of numbers and operations, in particular how these representations build from whole numbers to integers to fractions and decimals. Applying properties of numbers and operations in contextual situations, including measurement, and making reasonable estimates. Reasoning, communicating, and problem solving with numbers and operations. Applications to ratio, and connections with algebra. Taught primarily through student activities and investigations. Prerequisite(s): ENGL 111G and grade of C or better in MATH 120.

- MATH 112G. Fundamentals of Elementary Math II - 3 cr.
- Geometry and measurement. Multiple approaches to solving problems and understanding concepts in geometry. Analyzing and constructing two- and three-dimensional shapes. Measurable attributes, including angle, length, area, and volume. Understanding and applying units and unit conversions. Transformations, congruence, and symmetry. Scale factor and similarity. Coordinate geometry and connections with algebra. Reasoning and communicating about geometric concepts. Taught primarily through student activities and investigations. Prerequisite(s): C or better in MATH 111.

- MATH 120. Intermediate Algebra - 3 cr.
- Linear and algebraic functions as they arise in real world problems. Exponential and logarithmic functions. Equations and inequalities and their solutions considered symbolically, graphically and numerically. Prerequisite: adequate score on the Mathematics Placement Examination (see note above.)

- MATH 121G. College Algebra - 3 cr.
- Fundamental concepts of functions, including algebraic and graphical properties. Fitting functions to data. Finding zeroes and extreme values. Solving systems of equations. Prerequisites: Adequate math placement score or C or better in MATH 120.

- MATH 142G. Calculus for the Biological and Management Sciences - 3 cr. (2+2P)
- Review of functions. Derivatives, exponential and logarithmic functions, antiderivatives and indefinite integrals, basic ordinary differential equations and growth models, with an emphasis on applications. Includes a significant writing component. Prerequisite(s): C or better in MATH 121G.

- MATH 151. The Mathematics of Hydraulic Engineering - 3 cr.
- A combination of physical, mathematical, and computer simulation models will be developed to explore topics in hydraulic engineering that are central to environmental engineering applications. Same as CE 141. Prerequisite: MATH 121G or consent of instructor.

- MATH 152. Chemistry and Mathematics of the Molecular World - 3 cr.
- Introduction to chemical and mathematical concepts relevant to understanding the molecular world. Topics include atomic and molecular structure, intermolecular forces, physical states of matter, phase transitions, equations of motions, vectors, polynomial equations, and computer-based molecular modeling techniques. Same as CHEM 152. Prerequisite: MATH 121G or consent of instructor.

- MATH 175. Trigonometry - 3 cr.
- Trigonometric functions, graphs, identities, inverse functions, polar coordinates and applications. Complex numbers, curve fitting, roots of polynomials, exponential and logarithmic functions, conics, systems of equations and matrices. May not be taken for credit by students having credit for MATH 136. Prerequisite: C or better in MATH 121G. Restricted to Community Colleges only.

- MATH 190G. Trigonometry and Precalculus - 4 cr. (3+2P)
- Elementary functions used in the sciences with emphasis on trigonometric functions and their inverses. Polar coordinates. Complex numbers and Euler's formula. Analytic geometry and vectors. Prerequisite: adequate score on Mathematics placement exam or a C or better in MATH 121G (see note at beginning of this section).

- MATH 191G. Calculus and Analytic Geometry I - 4 cr.
- Algebraic, logarithmic, exponential, and trigonometric functions, theory and computation of derivatives, approximation, graphing, and modeling. May include an introduction to integration. Prerequisite(s): MATH 190G.

- MATH 192G. Calculus and Analytic Geometry II - 4 cr.
- Riemann sums, the definite integral, anti-derivatives, fundamental theorems, use of integral tables, numerical integration, modeling, improper integrals, differential equations, series, Taylor polynomials. Prerequisite(s): MATH 191G.

- MATH 200. Directed Study - 1-3 cr.
- Prerequisite: consent of the instructor. May be repeated for a maximum of 6 credits. Graded S/U.

- MATH 210G. Mathematics Appreciation - 3 cr.
- Mathematics and its role in the development and maintenance of civilization. Prerequisites: High school algebra, and an adequate score on the Mathematics Placement Examination.

- MATH 215. Fundamentals of Elementary Mathematics III - 3 cr.
- Probability, statistics, ratios, and proportional relationships. Experimental and theoretical probability. Collecting, analyzing, and displaying data, including measurement data. Multiple approaches to solving problems involving proportional relationships, with connections to number and operation, geometry and measurement, and algebra. Understanding data in professional contexts of teaching. Taught primarily through student activities and investigations. Prerequisite(s): C or better in MATH 112 and admittance into the TEP program.

- MATH 230. Matrices and Linear Programming - 3 cr.
- Linear algebra, linear programming and network models, with applications to the behavioral sciences. Prerequisite: C or better in MATH 121G.

- MATH 235. Calculus for the Technical Student I - 3 cr.
- Intuitive differential and integral calculus with applications to engineering. Prerequisite: C or better in MATH 190G.

- MATH 236. Calculus for the Technical Student II - 3 cr.
- A continuation and extension of the material in MATH 235. Prerequisites: C or better in MATH 235 or in MATH 192G.

- MATH 242. Calculus for the Biological and Management Sciences II - 3 cr.
- Calculus of functions of several variables, techniques of integration, differential equations, infinite series. Applications. Prerequisite: C or better in MATH 142G.

- MATH 275G. Spirit and Evolution of Mathematics - 3 cr.
- Same as HON 275G.

- MATH 278. Discrete Mathematics for Computer Science - 4 cr. (3+1P)
- Same as C S 278. Prerequisite: at least C or better in C S 171.

- MATH 279. Introduction to Finite Mathematics - 3 cr.
- Logic; sets, relations, and functions; introduction to mathematical proofs. Applications to computer science. Prerequisite: C or better in MATH 190G. (See note at beginning of this section.)

- MATH 280. Introduction to Linear Algebra - 3 cr.
- Systems of equations, matrices, vector spaces and linear transformations. Applications to computer science. Prerequisite(s): Grade of C or better in MATH 190G.

- MATH 291G. Calculus and Analytic Geometry III - 3 cr.
- Vector algebra, directional derivatives, approximation, max-min problems, multiple integrals, applications, cylindrical and spherical coordinates, change of variables. Prerequisite: grade of C or better in MATH 192G.

- MATH 292. Calculus and Analytic Geometry IV - 3 cr.
- Vector calculus, linear algebra, selected topics. Prerequisite: grade of C or better in MATH 291G or equivalent. Community Colleges only.

- MATH 300. Readings - 1-3 cr.
- A selection of readings and reports in the mathematical sciences, the breadth and depth of which is deemed to fit the needs of the student. Prerequisite: consent of instructor. Graded S/U.

- MATH 301. Special Topics - 1-3 cr.
- Specific subjects to be announced in the Schedule of Classes. May be repeated for a maximum of 12 credits.

- MATH 308. Supervised College Teaching - 1 cr.
- Skills for effective tutoring of precalculus mathematics within a mathematics learning center environment. Prerequisite: consent of instructor. Graded S/U.

- MATH 313. Fundamentals of Algebra and Geometry I - 3 cr. (3+1P)
- Covers algebra combined with geometry based on measurements of distance (metric geometry). Secondary mathematics education majors may take course as a math elective. MATH 313 does not substitute for other required math courses. Does not fulfill requirements for major in mathematics. Prerequisites: MATH 111 and MATH 112G.

- MATH 316. Calculus with Hands-on Applications - 3 cr.
- This course, primarily for prospective teachers, is taught in an interactive laboratory format. Students design and construct physical objects for which the planning stage requires calculus techniques. All numerical computations are carried out on graphing calculators. Meets simultaneously with MATH 516, primarily for practicing teachers. Secondary math education majors may take course as a math elective. MATH 316 does not fulfill requirements for majors in mathematics. Consent of instructor required.

- MATH 331. Introduction to Modern Algebra - 3 cr.
- Elements of abstract algebra, including groups, rings and fields. Prerequisite: C or better in MATH 279 and MATH 280.

- MATH 332. Introduction to Analysis - 3 cr.
- Development of the real numbers, a rigorous treatment of sequences, limits, continuity, differentiation, and integration. Prerequisite: C or better in MATH 192G and MATH 279.

- MATH 375. Business Applications - 3 cr.
- Matrix algebra and linear models, vector and matrix norms, applications to economics and statistics, linear programming, Lagrange multipliers and applications to economics, introduction to nonlinear programming, game theory. Computer software (Excel, LINDO and LINGO) will be introduced for solving numerical problems. Does not fulfill requirements for degrees in mathematics. Prerequisite(s): C or better in Math 142G, or in MATH 191G, or in Math 235.

- MATH 377. Introduction to Numerical Methods - 3 cr.
- Basic numerical methods for interpolation, approximation, locating zeros of functions, integration, and solution of linear equations. Computer-oriented methods will be emphasized. Prerequisites: grade of C or better in MATH 192G and some programming experience.

- MATH 391. Vector Analysis - 3 cr.
- Calculus of vector valued functions, Green's and Stokes' theorems and applications. Prerequisite: grade of C or better in MATH 291G.

- MATH 392. Introduction to Ordinary Differential Equations - 3 cr.
- Introduction to differential equations and dynamical systems with emphasis on modeling and applications. Basic analytic, qualitative and numerical methods. Equilibria and bifurcations. Linear systems with matrix methods, real and complex solutions. Prerequisite: C or better in MATH 192G or B or better in MATH 236.

- MATH 400. Undergraduate Research - 1-3 cr.
- Prerequisite: consent of faculty member. May be repeated for a maximum of 6 credits. Graded S/U.

- MATH 401. Special Topics - 1-3 cr.
- Specific subjects to be announced in the Schedule of Classes. May be used to fulfill a course requirement for the mathematics major. Prerequisite: An upper division MATH or STAT course, and consent of instructor.

- MATH 402. General Special Topics - 1-3 cr.
- Specific subjects to be announced in the schedule of classes. May not be used to fulfill a requirement for the mathematics major. Prerequisite: Consent of instructor

- MATH 411V. Great Theorems: The Art of Mathematics - 3 cr.
- Adopts the view of mathematics as art, using original sources displaying the creation of mathematical masterpieces from antiquity to the modern era. Original sources are supplemented by cultural, biographical, and mathematical history placing mathematics in a broad human context. Prerequisites: Grades of B or better in MATH 192G and any upper division MATH/STAT course, with overall GPA of 3.2 or better, or consent of instructor. Same as HON 411G.

- MATH 421. Financial Mathematics I - 3 cr.
- Types of derivatives, forwards and futures, options, returns and payoffs, Arrow-Debre, complete and incomplete markets, the one period model, the binomial option pricing model, binomial trees, martingales and sub martingales, Brownian motion, stochastic integrals, the Ito integral, Ito's dilemma, the Black-Scholes model, the Black-Scholes formula, European options, American options, free boundary problems, variational inequalities. This course is offered simultaneously with Math 521. Prerequisite: C or better in Math 280 or Math 480 and Stat 371 or consent of instructor.

- MATH 422. Financial Mathematics II - 3 cr.
- Bonds, swaps, exotic options, barrier options, Asian options, look back options, options with transaction costs, Fokker Plank theory, computing expectations, the Heath-Jarrow- Morton theorem, the Ho-Lee model, stochastic volatility models, exponential-affine models, numerical methods. This course is offered simultaneously with Math 522. Prerequisite: C or better in Math 421 or consent of instructor

- MATH 430. Combinatorial Mathematics - 3 cr.
- Methods for solving combinatorial construction and enumeration problems. Topics include Ramsey theory, generating functions, matchings, and block designs. Prerequisite: MATH 330 or MATH 331 or MATH 332.

- MATH 451. Introduction to Differential Geometry - 3 cr.
- Applies calculus to curves and surfaces in three dimensional Euclidean space. Prerequisites: MATH 280 and MATH 391, or consent of instructor.

- MATH 452. Foundations of Geometry - 3 cr.
- Topics in projective, axiomatic Euclidean or non-Euclidean geometries. Prerequisite(s): C or better in Math 331 or Math 332. Restricted to: Main campus only.

- MATH 453. Introduction to Topology - 3 cr.
- Introduction to topological spaces and metric spaces, with connections to analysis, geometry, and the classification of surfaces. Prerequisite: MATH 332 or consent of instructor.

- MATH 454. Mathematical Logic - 3 cr.
- Propositional calculus and the first order predicate calculus, including Godel's completeness theorem for the latter, and additional topics at the option of the instructor. Prerequisite(s): C or better in Math 331 or Math 332, or consent of instructor.

- MATH 455. Elementary Number Theory - 3 cr.
- Covers primes, congruences and related topics. Prerequisite: grade of C or better in MATH 331 or consent of instructor.

- MATH 457. Topics in Algebra - 3 cr.
- Topics may include coding theory, crytography, algebraic geometry, or symmetry groups. Prerequisites: C or better in Math 331.

- MATH 459. Survey of Geometry - 3 cr.
- Basic concepts of Euclidean geometry, ruler and compass constructions. May include topics in non-Euclidean geometry. For non-math majors. Prerequisite(s): C or better in Math 331 or Math 332. Restricted to: Main campus only.

- MATH 466. Lattice Theory - 3 cr.
- Introduction to partially ordered sets, distributive, modular, and Boolean lattices. Prerequisites: MATH 330 or MATH 331 or MATH 332 or consent of instructor.

- MATH 471. Complex Variables - 3 cr.
- A first course in complex function theory, with emphasis on applications. Prerequisite: MATH 391 or both MATH 392 and MATH 291G.

- MATH 472. Fourier Series and Boundary Value Problems - 3 cr.
- Fourier series and methods of solution of the boundary value problems of applied mathematics. Prerequisite: MATH 392.

- MATH 473. Calculus of Variations and Optimal Control - 3 cr.
- Euler's equations, conditions for extrema, direct methods, dynamic programming, and the Pontryagin maximal principle. Prerequisite: MATH 392.

- MATH 475. Business Applications - 3 cr.
- Taught with MATH 375 with additional work. Does not fulfill requirements for degrees in mathematics. Prerequisite(s): C or better in Math 142G, or in MATH 191G, or in Math 235.

- MATH 480. Matrix Theory and Applied Linear Algebra - 3 cr.
- An application driven course, whose topics include rectangular systems, matrix algebra, vector spaces and linear transformations, inner products, and eigenvalues and eigenvectors. Applications may include LU factorization, least squares, data compression, QR factorization, singular value decomposition, and search engines. Prerequisite(s): C or better in any 300-level course with a MATH or STAT prefix.

- MATH 481. Advanced Linear Algebra - 3 cr.
- Rigorous treatment of vector spaces and linear transformations including canonical forms, spectral theory, inner product spaces and related topics. Prerequisite: grade of C or better in MATH 331.

- MATH 491. Introduction to Real Analysis I - 3 cr.
- Rigorous discussion of the topics introduced in calculus. Sequences, series, limits, continuity, differentiation. Prerequisite: grade of C or better in MATH 332 or consent of instructor.

- MATH 492. Introduction to Real Analysis II - 3 cr.
- Continuation of MATH 491. Integration, metric spaces and selected topics. Prerequisite: MATH 491 or consent of instructor.

- MATH 498. Directed Reading - 1-6 cr.
- May be repeated for a maximum of 6 credits. Graded S/U.