# Course Offerings

**Jump to:**- Winter 2018
- Fall 2017
- Spring 2017

## Winter 2018▲

See complete information about these courses in the **course offerings database**. For more information about a specific course, including course type, schedule and location, click on its title.

### Calculus I

**MATH 101 - Dymacek, Wayne M.**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.

### Calculus I

**MATH 101 - McRae, Alan**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.

### Calculus II

**MATH 102 - Hardy, Stephen R.**

A continuation of MATH 101, including techniques and applications of integration, transcendental functions, and infinite series.

### Calculus II

**MATH 102 - Finch-Smith, Carrie E.**

A continuation of MATH 101, including techniques and applications of integration, transcendental functions, and infinite series.

### Introduction to Statistics

**MATH 118 - Hardy, Stephen R.**

Elementary probability and counting. Mean and variance of discrete and continuous random variables. Central Limit Theorem. Confidence intervals and hypothesis tests concerning parameters of one or two normal populations.

### Discrete Mathematics I

**MATH 121 - Keller, Mitchel T. (Mitch)**

A study of concepts fundamental to the analysis of finite mathematical structures and processes. These include logic and sets, algorithms, induction, the binomial theorem, and combinatorics.

### Multivariable Calculus

**MATH 221 - Beanland, Kevin J.**

Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

### Linear Algebra

**MATH 222 - Denne, Elizabeth J.**

Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.

### Linear Algebra

**MATH 222 - Finch-Smith, Carrie E.**

Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.

### Financial and Actuarial Mathematics

**MATH 270 - McRae, Alan**

Topics include the time value of money, the force of interest, annuities, yield rates, amortization schedules, bonds, contracts, options, swaps, and arbitrage. Equal emphasis is given to both the theoretical background and to the computational aspects of interest theory. This course helps prepare students for the Financial Mathematics actuary exam.

### Mathematical Statistics II

**MATH 310 - Dresden, Gregory P.**

Sampling distributions, point and interval estimation, testing hypotheses, regression and correlation, and analysis of variance.

### Real Analysis II

**MATH 312 - Abrams, Aaron D.**

Riemann integration, nature and consequences of various types of convergence of sequences and series of functions, some special series, and related topics.

### Abstract Algebra II

**MATH 322 - Dymacek, Wayne M.**

Rings, including ideals, quotient rings, Euclidean rings, polynomial rings. Fields of quotients of an integral domain. Further field theory as time permits.

### Abstract Algebra II

**MATH 322 - Finch-Smith, Carrie E.**

Rings, including ideals, quotient rings, Euclidean rings, polynomial rings. Fields of quotients of an integral domain. Further field theory as time permits.

### Partial Differential Equations

**MATH 333 - Feldman, Nathan S.**

An introduction to the study of boundary value problems and partial differential equations. Topics include modeling heat and wave phenomena, Fourier series, separation of variables, and Bessel functions. Techniques employed are analytic, qualitative, and numerical.

### Calculus on Manifolds

**MATH 345 - Denne, Elizabeth J.**

This course builds on material from both multivariable calculus and linear algebra. Topics covered include: manifolds, derivatives as linear transformations, tangent spaces, inverse and implicit function theorems, integration on manifolds, differential forms, and the generalized Stokes's Theorem.

### Directed Individual Study

**MATH 401 - Dresden, Gregory P.**

Individual conferences. May be repeated for degree credit if the topics are different.

Winter 2018, MATH 401-01: Topics in Continued Fractions (1). Prerequisite: Instructor consent required . A further study of number theory and continued fractions, with an emphasis on understanding the relationship between the roots of polynomials, and the collection of continued fractions with common tails. Dresden .

### Directed Individual Study

**MATH 401 - Dymacek, Wayne M.**

Individual conferences. May be repeated for degree credit if the topics are different.

Winter 2018, MATH 401-02: Military Engineering (1). Prerequisite: Instructor consent required. Graded course. Dymacek.

### Directed Individual Study

**MATH 401 - Dresden, Gregory P.**

Individual conferences. May be repeated for degree credit if the topics are different.

Winter 2018, MATH 401-03: Actuary Exam P Preparation (1). Prerequisite: Instructor consent required . A study of problem-solving techniques in preparation for the Society of Actuaries Exam P, whioch covers statistics and probabilty. Dresden.

### Directed Individual Study

**MATH 403 - McRae, Alan**

Individual conferences. May be repeated for degree credit if the topics are different.

Winter 2018, MATH 403-01: Directed Individual Study: Derivatives Markets (3). Prerequisite: Instructor consent. This course is designed to prepare students for Exam MFE (Models for Financial Economics) from the Society of Actuaries. McRae .

### Directed Individual Study

**MATH 403 - Keller, Mitchel T. (Mitch)**

Individual conferences. May be repeated for degree credit if the topics are different.

Winter 2018, MATH 403-02: Directed Individual Study: Number Theory (3). Prerequisite: Instructor consent. A study of the properties of integers. Topics include divisibility, congruences, prime numbers, the Euclidean algorithm, the Chinese Remainder Theorem, Fermat's Little Theorem, Euler's Theorem, Euler's phi function, the quadratic reciprocity law, and applications to encryption and data security. Keller .

## Fall 2017▲

See complete information about these courses in the **course offerings database**. For more information about a specific course, including course type, schedule and location, click on its title.

### Calculus I

**MATH 101 - Dymacek, Wayne M.**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.

### Calculus I

**MATH 101 - McRae, Alan**

### Calculus I

**MATH 101 - Hardy, Stephen R.**

### Calculus I

**MATH 101B - Dresden, Gregory P.**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.

Fall 2017, MATH 101B-01: Calculus I for Beginners: A First Course (3). Prerequisite: Instructor consent. This section meets 4 hours a week and is restricted to and specially tailored for those who are beginning their study of calculus. Students who have already seen calculus, yet wish to retake it, must register for MATH 101, 101E, or 101F instead of 101B. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (FM) Staff.

### Calculus I

**MATH 101E - Toporikova, Natalia**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.

Fall 2017, MATH 101E-01: Calculus I with Biology Applications (3). Prerequisite: Instructor consent. Corequisite: BIOL 111 or CHEM 110. This section meets 4 hours a week and has a strong emphasis on biological applications, and is intended to benefit students interested in biological majors and health-related careers. It is designed and specially tailored for First-Years who took high school biology and who are taking a lab-science course concurrently. It is intended both for those students who are beginning their study of calculus and for those who have seen some calculus but want to start over at the beginning of the calculus sequence. Mathematical concepts include the study of limits, derivatives, extrema, integrals, and the fundamental theorem of calculus. This section meets four days per week. (FM) Toporikova.

### Calculus I

**MATH 101F - Finch-Smith, Carrie E.**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.

Fall 2017, MATH 101F-01: Calculus and Environmental Data (3). This section meets 3 hours a week. The course covers the same calculus material as Math 101, namely the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. Applications in this section are focused on data collected by the Environmental Protection Agency and include discussions of finding an appropriate model for a data set and using calculus tools to analyze models. (FM) Staff.

### Calculus I

**MATH 101F - Finch-Smith, Carrie E.**

### Calculus II

**MATH 102 - Denne, Elizabeth J.**

A continuation of MATH 101, including techniques and applications of integration, transcendental functions, and infinite series.

### Calculus II

**MATH 102 - Hardy, Stephen R.**

### Discrete Mathematics I

**MATH 121 - Abrams, Aaron D.**

A study of concepts fundamental to the analysis of finite mathematical structures and processes. These include logic and sets, algorithms, induction, the binomial theorem, and combinatorics.

### Multivariable Calculus

**MATH 221 - Denne, Elizabeth J.**

Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

### Multivariable Calculus

**MATH 221 - McRae, Alan**

Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

### Multivariable Calculus

**MATH 221A - Beanland, Kevin J.**

### Linear Algebra

**MATH 222 - Beanland, Kevin J.**

Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.

### Mathematical Statistics I

**MATH 309 - Dresden, Gregory P.**

Probability, probability density and distribution functions, mathematical expectation, discrete and continuous random variables, and moment generating functions.

### Real Analysis I

**MATH 311 - Abrams, Aaron D.**

Basic properties of real numbers, elementary topology of the real line and Euclidean spaces, and continuity and differentiability of real-valued functions on Euclidean spaces.

### Abstract Algebra I

**MATH 321 - Dymacek, Wayne M.**

Groups, including normal subgroups, quotient groups, permutation groups. Cauchy's theorem and Sylow's theorems.

### Abstract Algebra I

**MATH 321 - Finch-Smith, Carrie E.**

Groups, including normal subgroups, quotient groups, permutation groups. Cauchy's theorem and Sylow's theorems.

### Ordinary Differential Equations

**MATH 332 - Feldman, Nathan S.**

First and second order differential equations, systems of differential equations, and applications. Techniques employed are analytic, qualitative, and numerical.

### Directed Individual Study

**MATH 401 - Denne, Elizabeth J. / Finch-Smith, Carrie E.**

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2017, MATH 401-01: GRE Prep (1) . Prerequisite: Instructor consent required. Preparation fo rthe Math GRE exam. Denne, Finch-Smith.

### Directed Individual Study

**MATH 401 - Hardy, Stephen R.**

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2017, MATH 401-02: Putnam Prep (1) . Prerequisite: Instructor consent required. An investigation of various problem-solving techniques in preparation for the Putnam math exam. Students are required to register for and take the Virginia Tech Regional Math Contest (October) and Putnam exam (the first Saturday of December) as part of this course. Hardy .

### Directed Individual Study

**MATH 401 - Dresden, Gregory P.**

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2017, MATH 401-03: Topics in Number Theory (1) . Prerequisite: Instructor consent required. Dresden .

### Directed Individual Study

**MATH 401 - Finch-Smith, Carrie E.**

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2017, MATH 401-05: Coverings of the Integers (1). Prerequisite: Instructor consent required. Students will explore coverings of the integers as a number theoretic tool, using both theoretical and computational methods. Applications of coverings will be emphasized, particularly in the construction of Sierpinski and Riesel numbers. Finch-Smith.

### Directed Individual Study

**MATH 401 - Beanland, Kevin J.**

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2017, MATH 401-06: Extreme Points for Banach Spaces (1). Prerequisite: Instructor consent required. Review of the literature regarding extreme points for Banach spaces and the lambda-propery of Aron and Lohman. In particular, will study results related to combinatorial Banach spaces. Beanland.

### Directed Individual Study

**MATH 403 - Dresden, Gregory P.**

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2016, MATH 403-01: Directed Individual Study: Derivatives Markets (3). Prerequisite: Instructor consent. This course is designed to prepare students for Exam MFE (Models for Financial Economics) from the Society of Actuaries. McRae.

## Spring 2017▲

See complete information about these courses in the **course offerings database**. For more information about a specific course, including course type, schedule and location, click on its title.

### FS: First-Year Seminar

**MATH 180 - Humke, Paul D.**

First-year seminar.

Spring 2017, Math 180-01: FS:A Brief Voyage to the 4th Dimension (4). First-Year Seminar. Prerequisite: First-Year class standing and MATH 102 or equivalent. A beginning look at the geometry of 4-dimensional Euclidean space, including learning some tools for studying 4-dimensional objects, and beginning to understand the difficulties in "seeing" such objects. Students also begin measuring in this 4-dimensional setting. The last week of the course is devoted to group projects and presentations. (SC) Humke.

### Fundamental Concepts of Mathematics

**MATH 301 - Denne, Elizabeth J.**

Basic analytical tools and principles useful in mathematical investigations, from their beginning stages, in which experimentation and pattern analysis are likely to play a role, to their final stages, in which mathematical discoveries are formally proved to be correct. Strongly recommended for all prospective mathematics majors.

### Fundamental Concepts of Mathematics

**MATH 301 - Keller, Mitchel T. (Mitch)**

Basic analytical tools and principles useful in mathematical investigations, from their beginning stages, in which experimentation and pattern analysis are likely to play a role, to their final stages, in which mathematical discoveries are formally proved to be correct. Strongly recommended for all prospective mathematics majors.

### Fundamental Concepts of Mathematics

**MATH 301 - Dresden, Gregory P.**

Basic analytical tools and principles useful in mathematical investigations, from their beginning stages, in which experimentation and pattern analysis are likely to play a role, to their final stages, in which mathematical discoveries are formally proved to be correct. Strongly recommended for all prospective mathematics majors.

### Seminar

**MATH 383 - Pommersheim, James E.**

Readings and conferences for a student or students on topics agreed upon with the directing staff. May be repeated for degree credit if the topics are different.

Spring 2017, MATH 383-01: Seminar: Quantum Algorithms (4). Prerequisite: MATH 301. An introduction to the theory of quantum computation with a focus on quantum algorithms. The class begins with a basic abstract mathematical formulation of quantum computation. Algorithms covered include the Deutsch-Jozsa algorithm, the Bemstein-Vazirani algorithm, Grover's search algorithm, and the Quantum Fourier Transform, leading up to Peter Shor's quantum factoring algorithm. Other topics may include quantum cryptography, quantum random walks, and the EPR paradox. Pommersheim