# Course Offerings

**Jump to:**- Spring 2017
- Winter 2017
- Fall 2016

## 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, Jamie**

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

## Winter 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 - Keller, Mitchel T. (Mitch)**

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

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (Note that 101, 101B, and 101E all lead into MATH 102 .) (FM) Staff.

MATH 101B: Calculus I for Beginners: A First Course (3). This class 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 101 or 101E 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. This section meets four days per week. (FM) Staff .

### Calculus II

**MATH 102 - Abrams, Aaron D.**

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

### Calculus II

**MATH 102 - Dymacek, Wayne M.**

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 - Feldman, Nathan S.**

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 - Dymacek, Wayne M.**

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.

### Linear Algebra

**MATH 222 - Richards, Trevor J.**

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

### Complex Analysis

**MATH 303 - Richards, Trevor J.**

Algebra of complex numbers, polar form, powers, and roots. Derivatives and geometry of elementary functions. Line integrals, the Cauchy Integral Theorem, the Cauchy Integral formula, Taylor and Laurent Series, residues, and poles. Applications.

### Real Analysis II

**MATH 312 - Dresden, Gregory P.**

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 - Bush, Michael R.**

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 - Finch-Smith, Carrie E.**

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.

### Modern Geometry

**MATH 342 - Abrams, Aaron D.**

A survey of recent developments in geometry. Topics vary and may include such subjects as the geometry of curves and surfaces, singularity and catastrophe theory, geometric probability, integral geometry, convex geometry, and the geometry of space-time.

### Combinatorics

**MATH 363 - Keller, Mitchel T. (Mitch)**

Topics include counting methods, permutations and combinations, binomial identities, recurrence relations. generating functions, special sequences, partitions, and other topics as time and student interest permit.

### Directed Individual Study

**MATH 401 - Denne, Elizabeth J.**

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

Winter 2017, MATH 401-01: Knot Theory (1). Prerequisite: Instructor consent . An introduction to Knot Theory studying classic knot invariants such as the Alexander and Jones polynomials. Denne.

### Directed Individual Study

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

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

Winter 2017, MATH 401-02: Directed Individual Study: Actuary Exam Prep (1). Prerequisite: MATH 118 or instructor consent. A study of problem-solving techniques in preparation for the Society of Actuaries Exam P. Finch-Smith.

### Directed Individual Study

**MATH 401 - Abrams, Aaron D.**

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

Winter 2017, MATH 401-03: Directed Individual Study: Continued Fractions (1). Prerequisite: Instructor consent. A study of the elementary theory of continued fractions, their history, and their applications Abrams .

## Fall 2016▲

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.

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (Note that 101, 101B, and 101E all lead into MATH 102 .) (FM) Staff.

MATH 101B: Calculus I for Beginners: A First Course (3). This class 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 101 or 101E 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. This section meets four days per week. (FM) Staff .

### Calculus I

**MATH 101 - Keller, Mitchel T. (Mitch)**

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

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (Note that 101, 101B, and 101E all lead into MATH 102 .) (FM) Staff.

MATH 101B: Calculus I for Beginners: A First Course (3). This class 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 101 or 101E 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. This section meets four days per week. (FM) Staff .

### Calculus I

**MATH 101 - McRae, Alan**

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (Note that 101, 101B, and 101E all lead into MATH 102 .) (FM) Staff.

MATH 101B: Calculus I for Beginners: A First Course (3). This class 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 101 or 101E 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. This section meets four days per week. (FM) Staff .

### Calculus I

**MATH 101 - Richards, Trevor J.**

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (Note that 101, 101B, and 101E all lead into MATH 102 .) (FM) Staff.

MATH 101B: Calculus I for Beginners: A First Course (3). This class 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 101 or 101E 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. This section meets four days per week. (FM) Staff .

### Calculus I

**MATH 101B - Abrams, Aaron D.**

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (Note that 101, 101B, and 101E all lead into MATH 102 .) (FM) Staff.

MATH 101B: Calculus I for Beginners: A First Course (3). This class 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 101 or 101E 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. This section meets four days per week. (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.

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. (Note that 101, 101B, and 101E all lead into MATH 102 .) (FM) Staff.

MATH 101B: Calculus I for Beginners: A First Course (3). This class 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 101 or 101E 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. This section meets four days per week. (FM) Staff .

Fall 2015, MATH 101E-01: Calculus I with Biology Applications (3). Prerequisite: Instructor consent . Corequisite: BIOL 111 or CHEM 110. This section 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 college lab science course concurrently. It is intended both for those students who have never had calculus before and also for those who have seen some calculus yet 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 II

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

### Calculus II

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

### Calculus II

**MATH 102 - Bush, Michael 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 - Richards, Trevor J.**

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

### Multivariable Calculus

**MATH 221 - Feldman, Nathan S.**

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.

### Real Analysis I

**MATH 311 - Dresden, Gregory P.**

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 - Bush, Michael R.**

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

### Ordinary Differential Equations

**MATH 332 - Finch-Smith, Carrie E.**

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

### Geometric Topology

**MATH 341 - McRae, Alan**

A study of the shape of space focusing on characteristics not detected by geometry alone. Topics are approached pragmatically and include point set topology of Euclidean space, map-coloring problems, knots, the shape of the universe, surfaces, graphs and trees, the fundamental group, the Jordan Curve Theorem, and homology.

### Graph Theory

**MATH 361 - Dymacek, Wayne M.**

Graphs and digraphs, trees, connectivity, cycles and traversability, and planar graphs. Additional topics selected from colorings, matrices and eigenvalues, and enumeration.

### 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 2016, MATH 401-01: Directed Individual Study: GRE Prep (1). Prerequisite: Instructor consent. Preparation to the Math GRE exam. Denne, Finch-Smith.

### Directed Individual Study

**MATH 401 - Bush, Michael R.**

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

Fall 2016, MATH 401-02: Directed Individual Study: Putnam Prep (1). Prerequisite: Instructor consent. 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. Bush.

### Directed Individual Study

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

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

Fall 2016, MATH 401-03: Directed Individual Study: Actuary Exam Prep (1). Prerequisite: MATH 118 or instructor consent. A study of problem-solving techniques in preparation for the Society of Actuaries Exam P. Dresden.

### Directed Individual Study

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

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

Fall 2016, MATH 401-04: Directed Individual Study: Statistical Inference (1). Prerequisite: Instructor consent. An advanced statistics course for those students planning on graduate school in statistics. Dresden.

### Directed Individual Study

**MATH 401 - Richards, Trevor J.**

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

Fall 2016, MATH 401-05: Directed Individual Study: Directed Graphs (1). Prerequisite: Instructor consent. Direct products of directed graphs. Richards.

### Directed Individual Study

**MATH 401 - Abrams, Aaron D.**

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

Fall 2016, MATH 401-06: Directed Individual Study: Algebraic Topology (1). Prerequisite: Instructor consent. An introduction to some of the algebraic invariants that are fundamental tools in modern topology. Abrams.

### Directed Individual Study

**MATH 403 - McRae, Alan**

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.