Discrete Mathematics Concentration

Prepare to Apply Math in the Real World

If you are interested in the real-world applications of numbers, discrete mathematics may be the concentration for you.

With a Bachelor of Science in Mathematical Sciences plus a concentration in discrete mathematics from Michigan Tech, you might contribute to advances in computing or make a career of preventing hackers from stealing valuable data. Fields that rely on discrete mathematics include computer science and cryptography.

Because discrete mathematics is the language of computing, it complements the study of computer science. The deep understanding of discrete mathematics that you gain in this program will provide a basis for applications in computing, especially in areas such as algorithms, programming languages, automated theorem proving, and software development.

Cryptography is the making and breaking of cryptosystems, with the goal of securing or unlocking data. Cryptographers create cryptosystems using algorithms to encrypt sensitive data, keeping it safe from hackers; cryptoanalysts unravel existing cryptosystems, decoding information. The National Security Agency, which is the largest single employer of mathematicians, and other intelligence agencies rely on cryptologists to protect national security, and financial institutions entrust these professionals with the safekeeping of vital data.

Another application of discrete mathematics is optimization, which industries employ to minimize their costs or maximize their profit. For instance, an airline could use optimization to determine how to schedule its flight crews in the most efficient manner. Other applications include communication theory, especially the study of error-correcting codes, and information theory.

Your concentration could prepare you for graduate work in computer science and mathematics, as well as for other careers requiring particular strength in discrete mathematics.

What is Discrete Math?

Discrete math is one of the oldest branches of mathematics, with a direct line of descent from problems studied in the most ancient mathematical texts. It includes number theory, the study of patterns in the whole numbers; graph theory, the study of structures and relations in sets; and abstract algebra and design theory, the study of symmetries. It is a good field for someone who sees the beauty in mathematics.

Get The Most From Discrete Mathematics

Degree requirements in discrete mathematics are intentionally kept low to maximize the flexibility of the program. Contact your advisor to talk about your options and read these tips to help you prepare for your career.

Use Free Electives To Customize Your Education

Use your free electives wisely to get the strongest possible degree. Free electives allow you to pursue an area of interest. Some options to consider:

You are strongly encouraged to complete a minor in computer science
It is also a good idea to complete a minor in a collateral field that has discrete mathematics connections, such as electrical engineering, chemistry, or biology.
Considering graduate school? You should take MA 4450 Real Analysis.
It may be also beneficial to acquire a knowledge of the basic concepts of statistics related to discrete mathematics. You could take MA 3720 Probability and MA 4720 Design and Analysis of Experiments, for example.

Speak to your advisor about the best way to use your free credits.

Get Summer Research Experience

There are many summer undergraduate research opportunities to explore. Besides gaining experience, participation in undergraduate research is a great way to decide if you want to go to graduate school (and it looks great on a graduate school application)! Consider:

The National Science Foundation (NSF) sponsors many Summer Research Experience for Undergraduates (REU) programs. Students participating in such a program work on research projects and typically receive free or greatly discounted room and board, along with a stipend of $2500–$4000.
Encourage Undergraduate Research
Michigan Tech faculty members also mentor student recipients of Summer Undergraduate Research Fellowships (SURF). Recipients get a stipend to work on a research project.

Complete an Internship or Participate in Enterprise

If you are planning to enter the workforce upon graduation, you will be more marketable if you do an internship or participate in Enterprise. For information about internships, contact University Career Services or your advisor.

Join a Professional Organization

Professional organizations offer learning and networking opportunities. The premier professional organization for discrete mathematicians is the Society for Industrial and Applied Mathematics (SIAM). Plus SIAM sponsors an annual conference on discrete mathematics. Michigan Tech students can join SIAM for free. Other professional organizations include:

Consult Other Online Resources

Some relevant online information about combinatorial mathematics, graph theory, and general discrete mathematics can be found at The Electronic Journal of Combinatorics and World Combinatorics Exchange.

Requirements

In addition to your core mathematics degree requirements, the following courses are required to complete your concentration in applied and computational mathematics:

Core Requirements

You must complete each of the following 12 credits:

MA 4208 - Optimization and Graph Algorithms

An introduction to linear and integer programming and related graph problems. Topics include simplex algorithm, duality, branch-and-bound and branch-and-cut, shortest paths, spanning trees, matchings, network flow, graph coloring, and perfect graphs.

Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Spring
Pre-Requisite(s): MA 3210

MA 4209 - Combinatorics and Graph Theory

An introductory course in combinatorics and graph theory. Topics include designs, enumeration, extremal set theory, finite geometry, graph coloring, inclusion-exclusion, network algorithms, permutations, and trees.

Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Fall
Pre-Requisite(s): MA 3210

MA 4310 - Abstract Algebra

Detailed study of abstract algebra: elementary number theory (congruences, quadratic residues, arithmetic functions), group theory (monoids, permutation groups, homomorphisms, quotients, Lagrange's theorem, finite abelian groups, Sylow's theorems), ring theory (domains, prime and maximal ideals, quotients, PID's), splitting fields, finite fields.

Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Spring
Pre-Requisite(s): MA 3310

MA 4330 - Linear Algebra

A study of fundamental ideas in linear algebra and its applications. Includes review of basic operations, block computations; eigensystems of normal matrices; canonical forms and factorizations; singular value decompositions, pseudo inverses, least-square applications; matrix exponentials and linear systems of ODEs; quadratic forms, extremal properties, and bilinear forms.

Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Fall
Pre-Requisite(s): (MA 2320 or MA 2321 or MA 2330) and MA 3160

Additional 6 Credit Requirement

You must complete two of the following:

MA 3202 - Introduction to Coding Theory

Transmission via noisy channels, hamming distance, linear codes, the ISBN-code, encoding and decoding, finite fields, Reed-Solomon codes, deep space communication, the compact disk code, sphere packing bound, hamming codes, hamming decoding.

Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Fall
Pre-Requisite(s): MA 2320 or MA 2321 or MA 2330

MA 3203 - Introduction to Cryptography

Topics include private-key cryptography, shift substitution, permutation and stream ciphers, cryptanalysis, perfect secrecy, public-key cryptography, and the RSA cryptosystem.

Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Spring, Summer
Pre-Requisite(s): MA 2320 or MA 2321 or MA 2330

MA 4908 - Theory of Numbers with Technology

Mathematical induction, Euclid's algorithm, prime and composite integers, algebra of congruences, Chinese remainder theorem, quadratic reciprocity law, number theoretic functions, first degree Diophantine equations, Pythagorean triples, Fermat and Mersenne numbers, factoring algorithms, tests for primality and various applications. Projects use Mathematica and EXCEL software packages.

Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Spring
Pre-Requisite(s): MA 3210 or MA 3310 or MA 3924

Tomorrow Needs Discrete Mathematicians With Strong Algorithmic Skills

In a world built almost entirely on discrete math, e.g. graph theory and combinatorics, your knowledge will be valuable across many disciplines: algorithms, cryptography, data structures, and more. You’ll develop and exercise skills crucial to solving complex problems, designing efficient algorithms, and optimizing systems. You’ll be prepared for success in computer science, cybersecurity, artificial intelligence, and data analysis. Your concentration in discrete mathematics is a pathway to a challenging, successful, and rewarding career.

Career Opportunities

Your future career options are unlimited with a degree in mathematics with a concentration in discrete mathematics. Career opportunities include:

Computer Modeling Specialist
Computer Scientist
Consultant
Cyber Security Analyst
Data Analyst
Data Scientist
Industrial Research and Development Specialist
Mathematician
Operations Research Analyst
Quantitative Research Analyst
Research Scientist
Simulation and Software Developer

Get Hired By

These are just some of the companies hiring mathematics majors with a concentration in discrete mathematics:

BTS Software Solutions
Canis Life Sciences
Capital One
HRL Laboratories
National Security Agency
Oracle
PepsiCo
Securian Financial

Pursue a Graduate Degree

These are just some of the graduate schools admitting Michigan Tech mathematics majors with a concentration in discrete mathematics:

Auburn University
Georgia Institute of Technology
University of Ottawa

American Mathematical Society Careers