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Undergraduate Mathematics Courses
Introductory 200-Level 300-Level 400-Level 500-Level

Current UM Course Offerings
Summer 2013 | Fall 2013 | Spring 2014

  Introductory Courses

MTH 099: Intermediate Algebra, 3 credits.
Fall & Spring Semester & First & Second Summer Session
Prerequisite: No prerequisite.
Description: This is a remedial algebra course intended to prepare students for MTH 101.
Topics: Review of arithmetic and operations on real numbers; properties of real numbers; algebraic expressions including: polynomials, factoring, rational expressions, radical expressions, integer exponents; solving linear equations and inequalities, including applications; graphs of linear equations and finding the equation of a line; systems of linear equations in two variables and applications; quadratic equations solved by factoring and the quadratic formula; basic introduction to function notation and applications with linear functions. NOTE: The grade and credits earned in this course are applied to the GPA, but the credits do not count towards the 120 credits needed for graduation.


MTH 101: Algebra for College Students, 3 credits.
Fall & Spring Semester & First & Second Summer Session
Prerequisite: ALEKS score ≥ 40 or passing grade in MTH 099.
Description: This course covers the fundamentals of college algebra, including algebraic expressions and equations, and an introduction to functions. This course is intended primarily for students in a BA program.
Topics: Review of the real number system and set operations; properties of real numbers; algebraic expressions including: polynomials, factoring, rational expressions, radical expressions, integer and rational exponents; division of polynomials; linear equations and inequalities, including applications; absolute value equations and inequalities; nonlinear inequalities; graphs of linear equations and finding the equation of a line; systems of linear equations in two and three variables with applications; systems of linear inequalities in two-variables; quadratic equations and applications; functions: including linear, quadratic, radical, cubic, and absolute value.


MTH 104: Geometry for Educators, 3 credits.
Offered By Announcement Only
Prerequisite: Passing grade in MTH 101 or adequate ALEKS score.
Description: Origins of geometry; topics from Euclidean, coordinate, and transformational geometry. Includes laboratory component. Only for pre-certification students in the School of Education who are not mathematics or science majors.


MTH 105: Algebra and Trigonometry, 5 credits.
Fall & Spring Semester
Prerequisite: ALEKS score ≥ 55 or passing grade in MTH 101.
Description: This course covers topics in algebra and trigonometry in order to prepare students for Calculus. This course combines the content of MTH 107 and MTH 108 in one semester. Students cannot receive credit for this course and MTH 107 or MTH 108. This course is intended primarily for students in the College of Engineering in order to prepare these students for MTH 151.
Topics: Review of algebraic manipulations of polynomials, exponential expressions, rational, and radical expressions; linear and quadratic equations; polynomial equations with solutions over the set of complex numbers; rational and radical equations; linear and nonlinear inequalities; equations and inequalities involving absolute value; graphs of equations; lines and circles; functions and graphs; mathematical models using functions; graphs of polynomial and rational functions; properties of division; Fundamental Theorem of Algebra; composition of functions; inverse functions; exponential and logarithmic functions and applications; trigonometric functions and their graphs; trigonometric identities; solving trigonometric equations; inverse trigonometric functions; law of sines; law of cosines; area and simple harmonic motion; polar coordinates, equations and graphs; the complex plane and De Moivre's Theorem; vectors and applications; the conic sections; systems of linear equations in two and three variables with applications.


MTH 107: Precalculus Mathematics I, 3 credits.
Fall & Spring Semester & First & Second Summer Session
Prerequisite: ALEKS score ≥ 55 or passing grade in MTH 101.
Description: This course covers topics in algebra, providing students with the fundamentals of precalculus. This course is intended for students who will eventually take Calculus. Not open to students with credit in MTH 105.
Topics: Review of the real number system and set operations; review of algebraic expressions, equations and inequalities, including: polynomials, rational expressions, radicals, absolute values, integer and rational exponents; division of polynomials; applications of equations and inequalities; the Division Algorithm and the Fundamental Theorem of Algebra. This course provides a concentration on functions including function notation, finding the domain and range of functions, implicit functions, shifts of basic functions, operations on functions; graphs of linear functions, absolute value functions, polynomial functions, rational functions, exponential functions, and logarithmic functions; defining the inverse function and finding the inverse of one-to-one functions; systems of linear equations in two and three variables with applications.


MTH 108: Precalculus Mathematics II, 3 credits.
Fall & Spring Semester & First & Second Summer Session
Prerequisite: Passing grade in MTH 107.
Description: This course covers topics in trigonometry and analytic geometry, providing students with the fundamentals of precalculus. This course is intended for students who will eventually take Calculus. Not open for students with credit in MTH 105.
Topics: Trigonometric functions and their graphs; trigonometric identities; solving trigonometric equations; inverse trigonometric functions; law of sines; law of cosines; area and simple harmonic motion; polar coordinates, equations and graphs; the complex plane and De Moivre's Theorem; vectors and applications; the conic sections.


MTH 113 (formerly 103): Finite Mathematics, 3 credits.
Fall & Spring Semester & First & Second Summer Session
Prerequisite: Minimum Math SAT score of 630 or ACT Math score of 28 or ALEKS score ≥ 60 or passing grade in MTH 101.
Description: This course is intended to provide students with exposure to a variety of mathematical ideas with an emphasis on real world applications. This course covers a selection of topics including sets, logic, counting techniques, probability, statistics, the mathematics of finance, and linear programming. The selection of topics may vary by instructor. This course is intended for BA Students and satisfies the General Education Requirement in Mathematics.
Topics: Selected topics from the following - sets; logic; combinations and permutations; probability; statistics; relations and functions; introduction to linear programming; matrices; finance.


MTH 130 (formerly 109): Introductory Calculus, 3 credits.
Fall & Spring Semester
Prerequisite: ALEKS score ≥ 65 or passing grade in MTH 107. Not for major or minor. Not for BS students.
Description: A one-semester survey of the fundamental principles of calculus; functions, limits, derivatives, definite integrals, applications.


MTH 140 (formerly 106): Calculus Concepts with Foundations A, 4 credits.
Fall Semester
Prerequisite: ALEKS score ≥ 65. Not open to students with credit in MTH 151, MTH 161, MTH 162, MTH 171, or MTH 172.
Description: Tools from algebra and trigonometry for calculus. Functions and graphs, limits and continuity, the derivative and applications.


MTH 141: Calculus Concepts with Foundations B, 4 credits.
Spring Semester
Prerequisite: C-minus or better in MTH 140.
Description: Tools from algebra, trigonometry, and analytic geometry for calculus. Further aspects of differentiation. Antiderivatives, definite integrals, and their applications.


MTH 151 (formerly 110): Calculus I for Engineers, 5 credits.
Fall & Spring Semester
Prerequisite: At least a C- in MTH 105 or ALEKS score ≥ 76 together with completion of high school trigonometry and analytic geometry. Not open to students with credit in MTH 141 or MTH 161 or MTH 171.
Description: Limits and continuity, derivatives, the definite integral, and applications relevant to engineering. Intended for students in Engineering or students taking PHY 205 concurrently.


MTH 161 (formerly 111): Calculus I, 4 credits.
Fall & Spring Semester & First & Second Summer Session
Prerequisite: At least a C- in MTH 108 or ALEKS score ≥ 76 together with completion of high school trigonometry and analytic geometry. Not open to students with credit in MTH 141 or MTH 151 or MTH 171.
Description: Limits and continuity, derivatives and applications, the definite integral and applications.


MTH 162 (formerly 112): Calculus II, 4 credits.
Fall & Spring Semester & First & Second Summer Session
Prerequisite: MTH 141 or MTH 151 or MTH 161. Not open to students with credit in MTH 172.
Description: Transcendental functions, methods of integration, L'Hôpital's Rule and improper integrals, infinite series, polar coordinates, and introduction to differential equations.


MTH 171 (formerly 131): Calculus I, 4 credits.
Fall Semester
Prerequisite: For students in the PRISM program. Not open to students with credit in MTH 141 or MTH 151 or MTH 161.
Description: The theory of limits, the derivative and the definite integral, techniques and applications. The sequence MTH 171-172 is more conceptually-oriented than MTH 161-162.


MTH 172 (formerly 132): Calculus II, 4 credits.
Fall & Spring Semester
Prerequisite: MTH 171. Not open to students with credit in MTH 162. Fall enrollment is for students with Advanced Placement credit in MTH 171.
Description: Continuation of MTH 171. Additional topics on the derivative and definite integral, improper integrals, infinite series, and introduction to differential equations.

  200-Level Courses

MTH 210: Introduction to Linear Algebra, 3 credits.
Fall & Spring Semester
Vectors, matrix algebra, systems of linear equations, and related geometry in Euclidean spaces. Fundamentals of vector spaces, linear transformations, determinants, eigenvalues, and eigenspaces.
Prerequisite or corequisite: MTH 162 or 172.

MTH 211: Calculus III, 3 credits.
Fall & Spring Semester & First Summer Session
Matrix algebra, vectors in space, partial differentiation, multiple integration.
Prerequisite: MTH 162 or 172. Not open to students with credit in MTH 310 or 433 or 533.

MTH 224: Introduction to Probability and Statistics, 3 credits.
Fall & Spring Semester & First Summer Session
Probability distributions, random variables, expectation and variance, point estimation, interval estimation, testing of hypothesis, analysis of variance.
Prerequisite or corequisite: MTH 162 or 172.

MTH 230: Introduction to Abstract Mathematics, 3 credits.
Fall & Spring Semester
Fundamentals of set theory, logic and methods of mathematical proof.
Prerequisite or corequisite: MTH 162 or 172.

  300-Level Courses

MTH 309: Discrete Mathematics I, 3 credits.
Fall & Spring Semester
Mathematical methods of computer science and computer engineering. Mathematical reasoning, sets, relations, functions, Boolean algebra, combinatorics, graphs.
Prerequisite: MTH 141 or 151 or 161 or 171.

MTH 310: Multivariable Calculus, 3 credits.
Fall & Spring Semester & First Summer Session
Equations of curves, surfaces, solids; vector differential calculus; integration of scalar functions. Applications.
Prerequisite: MTH 210 and (MTH 162 or 172). Not open to students with credit in MTH 433 or 533.

MTH 311: Introduction to Ordinary Differential Equations, 3 credits.
Fall & Spring Semester
Theory and applications for first-order differential equations. Linear differential equations. Solutions in series.
Prerequisite: MTH 162 or 172.

MTH 320: Introduction to Numerical Analysis, 3 credits.
Spring Semester
Interpolation, quadrature, numerical solution of algebraic and transcendental equations, and optimization.
Prerequisite: MTH 210 and (211 or 310).

MTH 359: Mathematical Models in Biology and Medicine, 3 credits.
Offered By Announcement Only
Fundamentals of the dynamical systems approach to modeling temporal change in biological systems. An introduction to the analysis of mathematical models in biology and medicine with detailed, concrete examples drawn from ecology, cell biology, neuroscience, and physiology.
Prerequisite: MTH 162 OR MTH 172 with grade of C- or better.

  400-Level Courses

MTH 433: Advanced Calculus, 3 credits.
Fall Semester
A rigorous and comprehensive treatment of the theoretical concepts of calculus. The real number system; sequences; series; continuity, differentiation and integration of functions of one variable.
Prerequisite: MTH 211 (or 310) and 230. Not open to students with credit in MTH 533.

MTH 461: Survey of Modern Algebra, 3 credits.
Spring Semester
Algebraic systems, equivalence classes, groups, rings, fields, unique factorization domains.
Prerequisite: MTH 210 and 230. Not open to students with credit in MTH 561.

MTH 471, 472: Directed Readings, 1-3 credits each.
Offered By Announcement Only
Topics selected from algebra, geometry, analysis, topology.
Prerequisite: Permission of department chairman.

  500-Level Courses

MTH 502: History of Mathematics, 3 credits.
Fall Semester
The development of mathematics from its earliest beginnings through the first half of the twentieth century. Numeral systems, geometry, algebra, analysis and set theory.
Prerequisite: Two courses in mathematics at the 200 level or above.

MTH 504: Foundations of Geometry, 3 credits.
Fall Semester
Axiom systems and models of Euclidean and Non-Euclidean geometry.
Prerequisite: MTH 230 or 309.

MTH 505: Theory of Numbers, 3 credits.
Offered By Announcement Only
Divisibility, primes; congruences; quadratic resides and reciprocity; Diophantine equations. Applications to cryptography.
Prerequisite: MTH 210 or 504.

MTH 506: Mathematical Logic, 3 credits.
Offered By Announcement Only
Logics, truth, proof, logical consequence, model theory, formalization, and computation. Meta-theory of first-order logic, computability theory, and Gödel's incompleteness theorems. Related results by Church, Turing, and Tarski. Discussion of their philosophical significance.
(co-listed with PHI 506 and CSC 506)
Prerequisite: MTH 230.

MTH 510: Linear Algebra, 3 credits.
Spring Semester
Abstract vector spaces, bases and dimensions, linear maps, eigen values and eigenvectors, inner product spaces, operators, spectral theorems, canonical forms.
Prerequisite: MTH 210; transition course in logical reasoning such as MTH 230 or 309 recommended but not required.

MTH 512: Elementary Complex Analysis, 3 credits.
Spring Semester
Complex variables; conformal mapping, contour integration.
Prerequisite: MTH 211 or 310.

MTH 513: Partial Differential Equations I, 3 credits.
Fall Semester
Derivation, well posedness, and qualitative properties of initial value and boundary value problems for the heat, wave and Laplace equations. Energy methods, causality, maximum principles, heat kernels, Fourier series, and potential theory.
Prerequisite: MTH 210, 310, and 311.

MTH 514: Partial Differential Equations II, 3 credits.
Spring Semester
Continuation of MTH 513. Approximations of solutions, distributions and integral transform methods, spectral theory and scattering. Applications to physical problems. Nonlinear equations and phenomena.
Prerequisite: MTH 513 or permission of the instructor.

MTH 515: Ordinary Differential Equations, 3 credits.
Fall Semester
Linear systems, equilibria and periodic solutions, stability analysis, bifurcation, phase plane analysis, boundary value problems, applications to engineering and physics.
Prerequisites: MTH 311 and either MTH 211 or 310.

MTH 516: Dynamics and Bifurcations, 3 credits.
Spring Semester
Bifurcation of equilibria and periodic solutions, global theory of planar systems, planar maps, nonlinear vibrations, forced oscillations, chaotic solutions, Hamiltonian systems, applications to engineering and physics.
Prerequisites: MTH 515 or permission of the instructor.

MTH 517: Data Structures and Algorithm Analysis, 3 credits.
Offered By Announcement Only
Basic algorithmic analysis. Algorithmic strategies. Fundamental computing algorithms. Distributed algorithms. Cryptographic algorithms. Geometric algorithms.
(Colisted with CSC 517.)
Prerequisite: MTH 309 (or 230) and CSC 220.

MTH 520: Numerical Analysis I, 3 credits.
Fall Semester
Topics from numerical linear algebra including solving systems of equations, LU, QR, and SVD factorizations, eigenvalues and eigenvectors, iterative methods, and applications.
Prerequisite: MTH 320 or permission of department chair.

MTH 521: Numerical Analysis II, 3 credits.
Offered By Announcement Only
Numerical solution of ordinary and partial differential equations.
Prerequisite: MTH 320 or 520 or permission of department chairman.

MTH 524: Introduction to Probability Theory, 3 credits.
Fall Semester
Probability spaces, random variables, expectation, limit theorems.
Prerequisite: MTH 224 and 310.

MTH 525: Introduction to Mathematical Statistics, 3 credits.
Spring Semester
Probability distributions, theory of sampling and hypothesis testing.
Prerequisite: MTH 524.

MTH 527: Theory of Computing, 3 credits.
Offered By Announcement Only
Sets, relations, and languages. Automata theory. Basic computability theory. Turing machines. The complexity classes P and NP.
(Colisted with CSC 527.)
Prerequisite: MTH 309 or 461.

MTH 528: Combinatorics, 3 credits.
Offered By Announcement Only
Permutations and combinations, generating functions, enumerative analysis.
Prerequisite: MTH 461 or 561.

MTH 531: Topology I, 3 credits.
Fall Semester
Set theory, topological spaces, compactness, connectedness, separation properties, quotient spaces, Tychonoff Theorem, compactification, Urysohn Lemma and Tietze Extension Theorem, function spaces.
Prerequisite: Permission of department chairman.

MTH 532: Topology II, 3 credits.
Spring Semester
Differential and topological manifolds, classical groups and associated manifolds, tangent and tensor bundles, vector fields, differential forms, transversality, Sard's theorem, Stokes' Theorem.
Prerequisite: MTH 210 and 531.

MTH 533: Introduction to Real Analysis I, 3 credits.
Fall Semester
Numerical sequences and series; continuity; differentiation; integration; sequences and series of functions; Fourier series; functions of several variables; implicit and inverse function theorems.
Prerequisite: MTH 211 (or 310) and 230.

MTH 534: Introduction to Real Analysis II, 3 credits.
Spring Semester
Continuation of MTH 533.
Prerequisite: MTH 533.

MTH 540: Algorithm Design and Analysis, 3 credits.
Offered By Announcement Only
Design techniques include divide-and-conquer, greedy method, dynamic programming, backtracking. Time and space complexity. Sorting, searching, combinatorial and graph algorithms.
(Colisted with CSC 540.)
Prerequisite: MTH 517 (or CSC 517).

MTH 542: Statistical Analysis, 3 credits.
Fall Semester
Statistical inference about one or two populations from interval, ordinal, and categorical data; analysis of variance; simple and multiple linear regression; designing research studies.
Prerequisite: MTH 210, 224.

MTH 547: Introduction to Mathematical Finance, 3 credits.
Offered By Announcement Only
Models of financial markets. Derivative securities: European and American options. Tools of mathematical finance: binomial trees, martingales, stopping times. Concepts of arbitrage and hedging. Risk-neutral valuation of financial derivatives; the Black-Scholes formula and its applications.
Prerequisite: MTH 224.

MTH 551: Introduction to Differential Geometry, 3 credits.
Offered By Announcement Only
Geometry of curves and surfaces in Euclidean space. Local space curve theory, intrinsic and extrinsic curvature of surfaces, geodesics, parallelism, and differential forms.
Prerequisite: MTH 210 and either MTH 211 or 310, or permission of instructor.

MTH 561: Abstract Algebra I, 3 credits.
Fall Semester
Groups, rings; linear algebra; modules.
Prerequisite: MTH 210 and permission of department chairman.

MTH 562: Abstract Algebra II, 3 credits.
Spring Semester
Continuation of MTH 561.
Prerequisite: MTH 561.

MTH 591-594: Topics in Mathematics, 1-3 credits each.
Offered By Announcement Only




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Department email: math@math.miami.edu
Webmaster email: webmaster@math.miami.edu
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