## 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:

- Mathematical Association of America (MAA)
- American Mathematical Society (AMS)
- Combinatorial Mathematics Society of Australasia (CMSA)
- Canadian Mathematical Society (CMS)

### 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:

### Additional 6 Credit Requirement

You must complete two of the following:

## 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