# Mathematics (MATH) Courses

This is the **2019-2020 UH Hilo catalog**, previous year catalogs can be viewed on the Back Issues page.

College of Natural and Health Sciences (CNHS)

See How to read course descriptions for information about the formatting used.

**MATH 100 Survey Of Math (3)** Survey of Mathematics course is intended primarily for non-science liberal arts majors to satisfy the university's quantitative reasoning requirement. Core topics include mathematical logic and mathematical thinking and problem solving. Additional topics may include number systems, computers, algebra, and probability. Pre: None. (Attributes: FQ, GQ)

**MATH 103 Intro to College Algebra (3)** For students who need to improve algebraic skills prior to taking Pre-calculus or Applied Calculus, or for courses in Introductory Chemistry, Physics or Statistics. Topics include exponents and radicals, factoring, systems of equations, linear equations, quadratic equations, general properties of functions, graphing, polynomial functions, exponential and logarithmic functions.

**MATH 111 MS Office Tools for Math & Sci (3)** Use of symbols, equations, images in scientific documents. Computations using spreadsheets with sums, averages, and scientific functions. Data analysis curve fitting, interpolation, statistics. Data presentation: visualization, charts, and graphs. Symbolic computation. Database processing: forms, queries, reports, VBA. Additional topics chosen from: real-time data acquisition, more advanced statistical methods, system simulation. Intended for science majors. Pre: Recommendation in Math Placement Test. (Same as CS 102) (Attributes: FQ, GQ)

**MATH 115 Intro to Stats and Prob (3) (lecture/lab)** Utilizes basic statistical topics including measures of central tendency and dispersion, classification of variables sampling techniques, elementary probability, normal and binomial probability distributions, tests of hypothesis, linear regression and correlation in order to solve problems. (Previously offered as MATH 121) (Attributes: FQ, GQ)

**MATH 125 Applied Calculus (3)** The course emphasis is on computations and applications to Business and Life Sciences. Topics include derivatives, curve sketching, optimization, exponential and logarithmic functions, integration and applications in these areas. Pre: C or better in MATH 103, or recommendation from the Math Placement Test. (Previously offered as MATH 115) (Attributes: FQ, GQ)

**MATH 135 Precalc: Elementary Functions (3)** Investigates linear, quadratic, polynomial, rational, exponential, logarithmic functions, and relevant topics. This course is the first part of the precalculus sequence. Pre: C or better in MATH 103, or an appropriate recommendation on the Math Placement Test. (Previously offered as MATH 104F) (Attributes: FQ, GQ)

**MATH 140 Precalc:Trig/Analytic Geometry (3)** Studies trigonometric functions, analytic geometry, polar coordinates, vectors, and related topics. The course is the second part of the precalculus sequence. Pre: C of better in MATH 135, or an appropriate recommendation on the Math Placement Test. Previously offered as MATH 104G (Attributes: FQ, GQ)

**MATH 140X Precalculus (4)** MATH 140X is an accelerated one semester course on the material covered in the sequence 135-140. Topics include the essential pre-calculus skils needed for success in calculus: functions, with special attention to polynomial, rational, exponential, logarithmic and trigonometric functions; plane trigonometry; and polar coordinates. Credit may not be earned for both MATH 140 and MATH 140X Pre: B+ or better in MATH 103, or C or better in Math 135, or an appropriate recommendation on the Math Placement Test. (Previously offered as MATH 104) (Attributes: FQ, GQ)

**MATH 241 Calculus I (4)** First half of a standard first year calculus sequence intended primarily for Natural Science majors. Topics include differential calculus, applications, and an introduction to integration. Pre: C or better in MATH 140X or MATH 140, or an appropriate recommendation on the Math Placement Test. (Previously offered as MATH 205). (Attributes: FQ, GQ)

**MATH 242 Calculus II (4)** Second semester of a standard first year calculus sequence intended primarily for Natural Science majors. Topics include applications of the definite integral, techniques of integration, an introduction to differential equations, and infinite series. Pre: C or better in MATH 241. (Previously offered as MATH 206) (Attributes: FQ, GQ)

**MATH 243 Calculus III (3)** Introduction to calculus of functions of several variables. Topics include partial differentiation; gradient, divergence, curl, and multi-variable optimization. Pre: C or better in MATH 242 (Previously offered as MATH 231). (Attributes: FQ, GQ)

**MATH 244 Calculus IV (3)** Introduction to calculus of functions of several variables. Topics include multiple integrals, line integrals, and surface integrals; Green's Theorem and Stoke's Theorem. Pre: C or better in MATH 243. (Previously offered as MATH 232).

**MATH 271 Applied Statistics with R (3)** Introduction to probability and statistics, with an emphasis on applied use of the R statistical computing system. Topics include categorical and quantitative random variables, probability distributions, descriptive statistics, estimation, hypothesis testing, and linear regression. Pre: C or better in MATH 135 or higher, or placement into MATH 140 or higher. Recommended: C or better in CS 171 or computer programming experience.

**MATH 300 Ordinary Diff Equations (3)** Theory and methods of solutions of ordinary differential equations and systems of linear differential equations with constant coefficients. Power series solutions, Laplace transforms, and applications. Pre: C in MATH 242.

**MATH 301 Partial Differential Equatns (3)** Construction and behavior of solutions of partial differential equations in physical and engineering applications, classical equations of mathematical physics, initial and boundary value problems, and eigenvalue problems. Pre: C in MATH 300 and MATH 243. Recommended: MATH 244 or concurrent.

**MATH 303 Complex Variables W/ Apps (3)** An introduction to the theory of functions of a complex variable. Complex differentiation and the Cauchy-Riemann equations. Analytic functions, conformal mappings, and Laufent series. Cauchy's Theorem, residue theory, and their applications. Additional topics include Reimann surfaces and the algebraic closure of the complex numbers. Pre: C or better in MATH 234. Recommended: C or better in MATH 244.

**MATH 310 Discrete Mathematics (3)** Topics from discrete mathematics, including logic, proof techniques, recurrence relations, set theory, combinatorics, relations, functions, graphs, Boolean algebraic structures and applications to coding theory. Pre: C or better MATH 242

**MATH 311 Intro Linear Algebra (3)** Algebra of matrices, linear equations, vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization and basic applications. Pre: C in MATH 242

**MATH 314 Topology (4)** A study of topological spaces and their continuous functions. A focus on properties of topologies, including compactness, Hausdorff, and connectedness. The construction of topologies, including the metric, quotient, product, and subspace topologies. Additional topics include manifold theory and functional analysis. Pre: C or better in MATH 242 or higher math course excluding MATH 271. Coreq: MATH 243

**MATH 317 Intro To Theory Of Equations (3)** Algebraic systems as related to solutions of polynomial equations, division algorithms and factorization for polynomials and integers, fundamental theorem of algebra, and related topics from elementary number theory including linear congruencies and rings of residue classes. Pre: C or better in MATH 310 or instructor's consent.

**MATH 324 Ring Theory (4)** An introduction to algebraic structures with two binary operations. A focus on the properties of the ring of integers, ring of integers modulo n, polynomial rings, and quotients of polynomial rings. Topics include the normal structure of rings: subrings; ideals, homomorphisms and quotients with focus on the above examples. Additional topics include an introduction of fields. Pre: C or better in MATH 242 or higher math course excluding MATH 271.

**MATH 360 Mathematical Physics (3)** Special functions of mathematical physics which arise from Sturm-Liouville equations: Bessel, beta, elliptical, gamma and Legendre functions. Generating functions, complex integral representations. Other topics may include integral transforms, Fourier analysis and linear algebra. Pre: MATH 244, or MATH 243 and 300 or instructor's consent. (Same as PHYS 360)

**MATH 371 Multivariate Modeling with R (3)** Multivariate statistical methods and model selection using R. Topics include the multivariate normal distribution and covariances, multiple regression, analysis of variance, principal component analysis, logistic regression, and decision trees. The course will emphasize model selection, and techniques such as validation sets to address the problem of overfitting. Pre: C or better in MATH 271.

**MATH 380 Chaos (3)** An introduction to nonlinear dynamical systems for science majors. Topics include dynamics in one and several dimensions, stability, excitable media, fractals, and time series analysis. Applications in physics, chemistry, ecology and other fields are illustrated. Pre: C or better in MATH 242 and C or better in PHYS 272 or Math 244. (Same as PHYS 380)

**MATH 407 Intro To Numerical Analysis I (3)** Solutions of equations in one variable, direct and iterative methods for systems of linear equations, the algebraic eigenvalue problem, interpolation and polynomial approximation, error analysis and convergence for specific methods. Offered spring semester. Pre: C in MATH 242 and MATH 311 and programming experience. (Same as CS 407).

**MATH 408 Intro To Numerical Analysis II (3)** A continuation of MATH 407. Topics will include approximation theory, numerical integration and differentiation, solution of systems of nonlinear equations, numerical solutions to differential equations. Pre: C in MATH 407. (Same as CS 408).

**MATH 421 Elem Probability Theory (3)** Sets, sample spaces, combinatorial probability, random variables, mathematical expectation, classical distributions applications. Pre: C or better MATH 242

**MATH 422 Elementary Math Statistics (3)** Statistical inference, estimation, hypothesis testing, regression, correlation, introduction to analysis of variance. Pre: C or better in MATH 421 and one of the following: MATH 115; or MATH 271; or instructor's consent.

**MATH 424 Group Theory (4)** An introduction to the theory of groups. Topics include the normal structure of groups: subgroups; normal subgroups, homomorphisms and quotients; direct products, and the structure of finite Abelian groups. Additional topics may include the Sylow theorems and/or Galois Theory. Pre: C or better in MATH 310, MATH 317, MATH 324, or MATH 431. Coreq: MATH 311

**MATH 431 Real Analysis I (4)** A rigorous axiomatic development of single variable calculus. Completeness, limits (functions, sequences, and series), continuity, differentiation, and integration. Topics covered: The real number system; the complete ordered field axioms with emphasis on completeness; sequences and series of real numbers, limits and continuity, differentiation, Riemann Integral, uniform and pointwise convergence. Pre: C or better in Math 310, Math 314, or MATH 424.

**MATH 432 Real Analysis II (4)** This course is a continuation of MATH 431, classical analysis concepts and theorems, including the topology of the real number and higher dimensional Euclidean spaces, convergence, continuity, uniform and pointwise convergence, differentiability, and integration Pre: C or better in MATH 431.

**MATH 441 Geometry I (3)** The course is specifically designed for future Math teachers. Emphasis is equally split between content and pedagogy of teaching high school Geometry. Topics include: foundations of Geometry, formal direct and indirect geometric proofs, geometric constructions, Euclidean Geometry in 2D and 3D. Pedagogy topics include: learning and practicing different teaching methods and techniques, developing lesson plans, teaching experience in a real classroom environment. Pre: C in MATH 243 and C or better in MATH 310, MATH 314, or MATH 324. Coreq: MATH 311

**MATH 442 Geometry II (3)** Axiomatic system-independence and consistency, advanced concepts in Euclidean geometry, elements of non-Euclidean geometries: spherical, elliptic, hyperbolic, introduction to classical Riemann geometry and modern geometry of manifolds. Pre: C or better in MATH 441 or instructor's consent.

**MATH 454 Modern Algebra I (3)** Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois Theory. Pre: C or better in MATH 310 and MATH 311 or instructor's consent. Recommended: MATH 317 and PHIL 345.

**MATH 455 Modern Algebra II (3)** This course is a continuation of Modern Algebra I. Pre: C or better in MATH 454.

**MATH 495A Seminar (1) (other)** Seminar presentations of topics in the physical sciences by faculty, enrolled students and invited speakers. The first semester (495A) is taken CR/NC; in the second semester (495B), students are required to present a seminar for a letter grade. Pre: senior standing or consent of instructor. (Same as ASTR 495A-495B, GEOL 495A-495B, CHEM 495A-495B and PHYS 495A-495B.)

**MATH 495B Seminar (1) (other)** Seminar presentations of topics in the physical sciences by faculty, enrolled students and invited speakers. The first semester (495A) is taken CR/NC; in the second semester (495B), students are required to present a seminar for a letter grade. Pre: senior standing or instructor's consent. (Same as ASTR 495A-495B, GEOL 495A-495B, CHEM 495A-495B, and PHYS 494A-494B).

**MATH 496 Tchg Assist & Tutoring Math (1–3)** Practice in individual tutoring and in the preparation of the selected topics in mathematics lecture or laboratory courses, under direct instructional supervision. This course may be repeated for a maximum of 6 credits and may not be used for substitution for any specific course or elective requirements of Mathematics major. Pre: consent of the supervisor and the department chair.

**MATH x94 Special Topics in Subject Matter (Arr.) (IO)** Special topics chosen by the instructor. Course content will vary. May be repeated for credit, provided that a different topic is studied. Additional requirements may apply depending on subject and topic.

**MATH x99 Directed Studies (Arr.) (IO)** Statement of planned reading or research required. Pre: instructor’s consent.