A List of Undergraduate Math Courses for Math Majors at UH



This is a list of Undergraduate Math Courses offered by the UH Math Department. Although there is a list of Undergraduate Math Courses on the Math Department website, the Math Department's list is incomplete and omits many important undergraduate math classes that are regularly offered. I have tried to make the list on this page more complete.

The Math Department's course catalog provides descriptions of the math courses offered and topics that appear in the syllabus. Here I provide descriptions of the courses that are aimed at math majors; in particular, I try to give you a sense of what the course and its subject matter are about (in case you are unfamiliar with the topic), and some advice and recommendations regarding whom the courses best serve.

Since the courses offered change from semester to semester, it is difficult to keep a list like this complete and up to date. So please let me know if you find omissions or errors in the list.

The links for the courses below take you to the Math Department's Course Description, when such a description exists, and to the Math Department's List of Undergraduate Courses when it does not.

No courses prior to Precalculus are listed here. See the Math Department's list of Undergraduate Courses for a list with course descriptions of math courses prior to Precalculus.




Undergraduate Math Courses at UH

Course Number Course Title Short Description and Relevance for Math Majors
Math 1330
Precalculus This course is a preparation for Calculus
Math 1431 Calculus I This course studies derivatives of functions, including rates of change and tangent lines. It ends with an introduction to the integral.
Math 1432 Calculus II This course contains a further study of integrals. It also includes an introduction to sequences and series of real numbers.
Math 1450 Accelerated Calculus I Math 1450 and Math 1451 include topics covered in Math 1431, Math 1432, and Math 2433. The pace is faster then in the Math 1431--Math 1432 sequence, and topics are also covered in more depth.
Math 1451 Accelerated Calculus II Math 1450 and Math 1451 include topics covered in Math 1431, Math 1432, and Math 2433. The pace is faster then in the Math 1431--Math 1432 sequence, and topics are also covered in more depth.
Math 2331 Linear Algebra The study of matrices, vector spaces, and linear transformations. This is an important course for math majors (and useful in many other disciplines) and should be taken as soon after Calculus II as possible.
Math 2433 Calculus III This course is also called Multivariable Calculus or Calculus in Higher Dimensions. While one variable calculus (i.e., Calculus I and II) studies functions f : R --> R from the real numbers to the real numbers, in multivariable calculus one studies functions f : Rn --> Rm and examines derivatives and integrals of these multivariable functions.
Math 3311 Functions and Modeling This course is primarily for math majors in teachHOUSTON or intending to become certified to teach high school mathematics. It covers ideas and activities that reinforce interrelationships among topics in mathematics, especially as taught in secondary education. Themes that recur throughout the course are transformations, data analysis methods, and technology. This course satisfies the Writing in the Disciplines core requirement.
Math 3321 Engineering Mathematics This course is primarily for non-majors, and should be skipped by most math majors. It covers a condensed version of the material in Math 2331 and Math 3331.
Math 3325 Transition to Advanced Mathematics This course is an introduction to proofs and the abstract approach that characterizes upper level mathematics courses. It serves as a transition into advanced mathematics, and should be taken after the initial calculus sequence and before (or concurrently with) mid-level mathematics courses. The goal is to give students the skills and techniques that they will need as they study any type of advanced mathematics, whether it be in pure mathematics, applied mathematics, or application-oriented courses. In particular, this course covers topics that are ubiquitous throughout mathematics (e.g. logic, sets, functions, relations) and helps prepare students for classes such as Real Analysis, Abstract Algebra, and Advanced Linear Algebra, that are required for majors and minors. A major objective of the course will be to teach students how to read, write, and understand proofs. Throughout the course students will be exposed to the notation, language, and methods used by mathematicians, and will gain practice using these in their own proofs. In addition, great emphasis is placed on writing and communication.
Math 3330 Abstract Algebra This course is an introduction to Abstract Algebra, which is one of the major areas of mathematics. It focuses on the study of groups and rings, which are abstract objects used to generalize the operations of "addition" and "multiplication" from basic arithmetic. Proofs are used throughout the course. Abstract Algebra is one of the cornerstones of modern mathematics, and is used extensively in both pure and applied math. This course is required of all math majors.
Math 3331 Ordinary Differential Equations Differential equations are equations involving derivatives of a function. This course teaches methods for finding functions that are solutions to certain kinds of differential equations. This particular course tends to be computational and uses many of the differentiation and integration techniques learned in Calculus I and II. Differential equations come up in many real-world applications of mathematics, and are useful in modeling. This is a great course for students interested in engineering, physical or biological sciences, economics, finance, or careers in industry.
Math 3333 Intermediate Analysis Real Analysis is a subject that takes a rigorous approach to the concepts studied in Calculus, such as convergence, limits of functions, continuity, differentiability, and integrability. The rigorous approach involves a great deal of proofs, however the course is far more than simply "providing proofs of the things we learned in Calculus I and II". The new techniques developed through the rigorous approach allow methods for computing things that were inaccessible in Calculus I and II, and also provide qualitative and approximate results when precise ones are unavailable. Real Analysis is one of the cornerstones of modern mathematics, and is used extensively in both pure and applied math. In addition, many advanced math classes at UH build off of the material in Math 3333. This course is required of all math majors.
Math 3334 Advanced Multivariable Calculus This course is a continuation of the material learned in Multivariable Calculus (Math 2433), and involves a more detailed analysis of differentiation and integration of multivariable functions f : Rn --> Rm. The material involves a mixture of proofs and computations. In many universities the material in Math 2433 and Math 3334 is combined into one course, but at UH it is done in two. The material of this course has significant overlap with the material in Math 3335, and students should take one of Math 3334 or Math 3335, but not both. Math majors who are not also double majoring in physics or engineering should take Math 3334 rather than Math 3335.
Math 3335 Vector Analysis This course is very similar to Math 3334, but has more emphasis on the integration theorems for multivariable functions. It is primarily a service course for students majoring in physics and engineering, and it was developed as an alternate version of Math 3334 to cover integration theory in more detail so that these students can get a better mathematical background for the integration results required in such physics courses as electromagnetic field theory. The material involves a mixture of proofs and computations. In many universities the material in Math 2433 and Math 3334 is combined into one course, but at UH it is done in two. The material of this course has significant overlap with the material in Math 3334, and students should take one of Math 3334 or Math 3335, but not both. Math majors who are not also double majoring in physics or engineering should take Math 3334 rather than Math 3335.
Math 3336 Discrete Mathematics Discrete mathematics is the study of mathematical structures that are isolated and discrete, rather than varying in a smooth or continuous way. In contrast to subjects such as calculus or real analysis, where the continuum of real numbers or smooth (i.e., continuous or differentiable) functions are studied, in discrete mathematics one studies objects such as integers, graphs, and statements in logic that have distinct, separated values. While discrete mathematics is a subject studied by many mathematicians, this particular course at UH is primarily a service course for Computer Science students, and there is significant overlap with Math 3325: Transition to Advanced Mathematics. Math majors should not take this course, and should instead take Math 3325. Math majors interested in learning more about discrete mathematics can take Math 4315: Graph Theory with Applications.
Math 3338
Probability This is a course in mathematical probability theory, and it also teaches applications to real-world problems in subjects such as Finance, Insurance, and Engineering. The material involves a mixture of proofs and computations.
Math 3339
Statistics for the Sciences This is a course in mathematical statistics, and it also teaches applications to real-world problems in subjects such as Finance, Engineering, and the Sciences. The material involves a mixture of proofs and computations.
Math 3340
Introduction to Fixed Income Mathematics This is a course in the mathematical modeling of finance. It shows how calculus-level mathematics may be used to determine costs, prices, and returns in various standard "fixed income problems" including the basic analysis of loans, bonds, and portfolios. This is a useful course for anyone interested in Financial Mathematics.
Math 3363 Introduction to Partial Differential Equations While the Ordinary Differential Equations (ODEs) studied in Math 3331 involve functions of one variable, Partial Differential Equations (PDEs) are equations involving functions of more than one variable and their (partial) derivatives. This course in an introduction to PDEs and boundary value problems, including such topics as Fourier series, the heat equation, vibrations of continuous systems, the potential equation, and spectral methods. This is a good course for students interested in engineering, physical or biological sciences, economics, finance, or careers in industry. PDEs are used in many aspects of mathematical modeling that arise in real-world problems. Math majors interested in a more serious treatment of PDEs may wish to skip this course and instead take the Math 4335--Math 4336 sequence (or only Math 4335, if desired).
Math 3364 Introduction to Complex Analysis Whereas Calculus I and II studies differentiation and integration of functions going from the real numbers to the real numbers f:R --> R, complex analysis studies differentiation and integration of functions f: C --> C from the complex numbers to the complex numbers. This turns out to be fairly different from studying the calculus of real-valued functions, or even functions f:R2 --> R2, and many results for differentiable complex functions are very strong and beautiful, resulting in a very rich theory. In mathematics, the subject of Analysis is often divided into three main areas: Real Analysis, Complex Analysis, and Functional Analysis. This course is one of the only opportunities for math majors at UH to gain exposure to an area of analysis outside of real analysis. (Math 3333, Math 4331, and Math 4332 cover Real Analysis, and Functional Analysis is typically not covered until graduate school.) All math majors who want to go to graduate school in mathematics or a related subject should take this course. In addition, complex analysis has application in physics, particularly to some aspects of hydrodynamics and thermodynamics as well as in nuclear, aerospace, mechanical and electrical engineering. Therefore, certain physics or engineering students may also be interested in this course.
Math 3379 Introduction to Higher Geometry This course is primarily for math majors in teachHOUSTON or intending to become certified to teach high school mathematics. Topics include synthetic and algebraic geometry, harmonic division, cross ratio, and groups of projective transformations. This course satisfies the Writing in the Disciplines core requirement.
Math 3396 Senior Research Project This is essentially an independent study course in which you work on a project under the supervision of a professor.
Math 3397 Selected Topics in Mathematics This is the course number assigned to a class that a professor wishes to teach, but which does not currently exist in our curriculum. The topic of the course depends on who is teaching it, and no two Math 3397 courses are the same.
Math 3399 Senior Honors Thesis This is course in which you can work on a research project with under the supervision of a professor.
Math 4309
Mathematical Biology Mathematical Biology (also sometimes called Theoretical Biology) is an interdisciplinary subject where mathematics is used to study biological processes. It includes at least four major subfields: (1) biological mathematical modeling, (2) relational biology/complex systems biology, (3) bioinformatics, and (4) computational biomodeling/biocomputing. Mathematical biology aims at the mathematical representation, treatment, and modeling of biological processes, using a variety of applied mathematical techniques and tools. It has both theoretical and practical applications in biological, biomedical, and biotechnology research. This course introduces a variety of discrete and continuous ordinary and partial differential equation models of biological systems. Mathematical methods taught include phase plane analysis, bifurcation methods, separation of timescales, and some scientific computing in MATLAB. Biological topics include population dynamics, epidemiology, gene networks, neuroscience, and biological transport.
Math 4310
Biostatistics Biostatistics (also called biometrics) is the application of statistics to a wide range of topics in biology. The subject of biostatistics encompasses the design of biological experiments, especially in medicine, pharmacy, agriculture, and fishery; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from, the results. A major branch of biostatistics is medical biostatistics, which is exclusively concerned with medicine and health.
Math 4315
Graph Theory with Applications A graph is a mathematical structure used to model pairwise relations between objects. The definition of a graph is very simple: A graph consists of "dots" (formally called vertices) and "lines" (formally called edges) drawn between them. A graph may be undirected, meaning that there is no distinction between the two vertices on each edge, or it may be directed, with its edges written as an arrow pointing from one vertex to another. Graphs are ubiquitous and arise in numerous subjects where discrete relations between objects are found. Graphs are particularly useful in computer science, and they are the main object of study in the subject of Discrete Mathematics. Topics covered in this course include Konigsburg Bridges and Eulerian tours with possible applications to reconstruction of DNA sequences, Euler's characteristic formula, planar graphs with application to fullerenes, the 4-color problem and a proof of 5-color theorem, selected graph invariants (including chromatic, independence, and the matching numbers with applications), Ramsey Theory with application to the Foundations of Mathematics, Erdös's probabilistic method, and the eigenvalues of graphs.
Math 4320
Introduction to Stochastic Processes In probability theory, a stochastic process (also called a random process) is a collection of random variables used to represent the evolution of a system over time. Unlike a deterministic process in which the system can only evolve in one way (as in the case, for example, of solutions of an ordinary differential equation), in a stochastic process there is some indeterminacy: even if the initial condition (or starting point) is known, there are several (often infinitely many) directions in which the process may evolve. This course is an introduction to stochastic processes, and it covers such topics as Markov chains, Poisson processes, renewal phenomena, Brownian motion, and an introduction to stochastic calculus.
Math 4331-Math 4332
Introduction to Real Analysis Math 4331 and Math 4332 comprise a senior sequence in Real Analysis. This course builds off the material in Math 3331, and instead of requiring functions to go from the reals to the reals f:R --> R, one considers functions between metric spaces (i.e., abstract spaces in which one has a notion of "distance"). For these functions between metric spaces one introduces and studies concepts such as convergence, continuity, differentiation, and integration. The results proven in this course contain certain results from Math 3331 as well as results from Multivariable Calculus as special cases, but at the same time the more general results from this course apply to new situations and have novel applications. It also provides an introduction to point-set topology in metric spaces and in Rn. Analysis is one of the main branches of Mathematics, and Real Analysis is the cornerstone for studying many advanced topics in mathematics. This course should be taken by all math majors considering graduate school in mathematics. It should also be taken by all math majors considering graduate study in Economics, Finance, or any discipline involving Probability. (Real Analysis is a prerequisite for graduate-level study of Measure Theory, a topic used in many areas of mathematics, as well as in Probability Theory and Economics.)
Math 4335-Math 4336 Partial Differential Equations The material in this course is similar to Math 3363, but gives a more advanced treatment of the subject. While the Ordinary Differential Equations (ODEs) studied in Math 3331 involve functions of one variable, Partial Differential Equations (PDEs) are equations involving functions of more than one variable and their (partial) derivatives. This course studies PDEs and boundary value problems, including such topics as Fourier series, the heat equation, vibrations of continuous systems, the potential equation, and spectral methods, as well as a number of advanced topics. PDEs are used in many aspects of mathematical modeling that arise in real-world problems, and the study of PDEs forms the cornerstone of many aspects of Applied Mathematics.
Math 4350-Math 4351 Differential Geometry Differential Geometry uses the techniques of differential and integral calculus, as well as linear algebra, to study problems in geometry. The objects of study include curves, surfaces, and higher-dimensional analogues in Euclidean space. Differential Geometry is closely related to Differential Topology, and to the geometric aspects of the theory of differential equations.
Math 4355 Mathematics of Signal Representations This course is an introduction to the subject of Signal Processing, which deals with the generation, transformation, and interpretation of information. The signals involved could be real-world signals such as audio, visual, temperature, pressure, or position that have been digitized and described as mathematical signal representations. One then wishes to modify, analyze, or otherwise manipulate the information contained in such signal representations. The main tools introduced in this course are Fourier Series and Wavelets. Signal Processing is a subject that in many ways lies at the intersection of pure and applied mathematics --- many of the techniques it uses require deep and beautiful abstract results from real analysis and linear algebra, while at the same time there are numerous real-world applications and many of the problems studied are motivated by physical situations.
Math 4362 Theory of Ordinary Differential Equations This is a second course in Ordinary Differential Equations (i.e., differential equations for functions of one variable). It is meant to be taken after Math 3331.
Math 4364--4365 Numerial Analysis Numerical Analysis is the study of algorithms that use numerical approximation to study problems from mathematical analysis. In many situations (e.g., solving large systems of linear equations, solving to differential equations, integration), exact answers are often impossible to obtain in practice. Numerical Analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors. Numerical Analysis naturally finds applications in engineering and the physical sciences. However, recent decades, Numerical Analysis has also found applications in biology and medicine (e.g., stochastic differential equations and Markov chains used to model living cells), actuarial science (e.g., in approximation done in actuarial analysis and insurance pricing), and financial mathematics (e.g., to calculate the value of stocks and derivatives more precisely than other market participants).
Math 4377 - 4378
Advanced Linear Algebra I & II This course can be viewed as an advanced counterpart to Math 2331. At the beginning of this sequence, many topics from Math 2331 are revisited (e.g., matrices, vector spaces, linear transformations, change of basis, diagonalization) with greater emphasis on working in abstract vector spaces and more attention to proofs. Later in the sequence, additional topics such as Jordan canonical form and basic module theory are studied. Algebra is one of the main branches of Mathematics (together with Analysis and Topology), and this is a good course for math majors considering graduate study in mathematics.
Math 4380
A Mathematical Introduction to Options This course is an introduction to financial economics and derivatives. It surveys fundamental ideas underlying the financial mathematics and the roles played by options, futures, and forwards in risk management. It introduces the notions of geometric Brownian motion, jump diffusion processes, risk-neutral valuation principle, Arrow-Debreu securities, binomial models, stochastic volatility, and martingales. There is typically some computer use throughout the course. Students who plan to take the actuarial exams will benefit from the material covered in this course.
Math 4383
Number Theory Number Theory may be thought of as a mathematical study of deep ideas that originated in basic arithmetic. It includes such topics as properties of the integers, the study of prime numbers, and methods for factoring large numbers into primes. Number Theory studies the integers, as well as objects made out of integers (e.g., rational numbers), and generalizations of the integers (e.g., algebraic integers). Integers can be considered either in themselves or as solutions to equations certain equations (e.g., Diophantine equationsy). Questions in number theory are sometimes best understood through the study of analytical objects (e.g., the Riemann zeta function) that encode properties of the integers, and this approach is called Analytic Number Theory. One may also study generalizations of numbers using abstract algebra, and this approach is known as Algebraic Number Theory. This topics of the course include divisibility theory, primes and their distribution, theory of congruences, Fermat's Little Theorem, number theoretic functions, Euler's Phi-function, Euler's Theorem, primitive roots, quadratic reciprocity, nonlinear Diophantine equations, and other topics if time permits.
Math 4388
History of Mathematics This course is taught online. It provides a college-level introduction to the history of mathematics. Topics covered include critical historical mathematics events, such as creation of classical Greek mathematics and development of calculus, as well as lives of notable mathematicians, such as Fermat, Descartes, Newton, Leibniz, Euler, and Gauss, and the impact of their discoveries. Goals for the course are for students to (1) learn about the history of mathematics; (2) learn about the philosophy of mathematics and its development throughout history; (3) gain an appreciation for the effort and great contributions of past generations; (4) gain a better appreciation for the current state of mathematics; (5) obtain inspiration for mathematical education and the further development of mathematics.
Math 4389
Survey of Mathematics This course is meant to be taken by students near the end of the undergraduate math major. It reviews material learned in various courses, and examines how the different material is related, giving a top-down view of the subjects one has learned throughout the major. The format of the course is a sequence of two-to-three week modules reviewing some of the most important concepts in undergraduate mathematics. Topics from Calculus, Linear Algebra, Differential Equations, Abstract Algebra, Analysis, and Probability are discussed.
Math 4399 Senior Honors Thesis This is course in which you can work on a research project with under the supervision of a professor.


You can also look at the list of graduate courses offered in the UH math department. It is possible for undergraduates to take graduate courses. In addition, the online list of graduate courses often includes a list of the 4000-level undergraduate courses that are offered in the upcoming semesters.




The list above omits the following courses:

Math 2303: Concepts in Algebra
Math 2311: Introduction to Probability
Math 3303: Elements of Algebra and Number Theory
Math 3304: Elements of Mathematical Analysis
Math 3305: Formal and Informal Geometry
Math 3306: Problem Solving In Mathematics
Math 3307: Statistical Applications
Math 3310: History of Mathematics

because these course are intended for non-majors. In fact, none of them may be applied toward GPA or course requirements for math majors/minors.







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