# Mathematics and Statistics Advising Guide

## What is Mathematics and Statistics?

Mathematics and Statistics are rich areas of inquiry ranging from pure abstractions to concrete applications.  The language of Mathematics is remarkably powerful and flexible, and the modes of thinking learned in Statistics can yield remarkable insight into many situations that pervade modern life. The ideas of Mathematics and Statistics are not only beautiful and valuable in themselves but also relevant to almost all disciplines, including but not limited to Biology, Chemistry, Computer Science, Economics, Environmental Studies, and Physics.

# Career Opportunities in Mathematics and Statistics

Studying Mathematics and Statistics develops such skills as arguing logically and rigorously, thinking abstractly, formulating and solving problems, analyzing data, and creating and analyzing mathematical models. Employers value these skills;  consequently, mathematics and statistics majors find themselves in demand by employers for careers in a wide spectrum of fields.

A bachelor's degree in mathematics and statistics will prepare you for jobs in statistics, actuarial sciences, mathematical modeling, cryptography, and mathematics education, as well as for graduate school leading to a research career in engineering, computer science, mathematics, or statistics. A strong background in mathematics and statistics is also necessary for research in many areas such as biomedical sciences, computer science, and social sciences. A few of the many fields where mathematics and statistics majors are in demand are described below.

### Mathematical and Statistical Modeling

In mathematical modeling, you write down equations to describe how a real world system behaves. The "system" might be drawn from many different fields. For example, most financial companies hire mathematicians to study financial models and make predictions based on statistical evidence. In physics or engineering you might be interested in how heat is dissipated through the heat shield of a space vehicle. In physiology you might want to apply the laws of fluid dynamics to describe how blood flows in vessels and what happens when blood pressure is increased. In economics you might want to predict how a strike in the automotive industry will affect other parts of the economy.

Building a mathematical model is usually a multi-stage process: you study the problem, write down the equations, use them to predict what will happen, see if your predictions agree with experiments, modify your equations if necessary, make new predictions, and so on.

The model may be solved exactly (you may be able to write down a function that tells you the values you want to know), or you may have to approximate the values because they can't be found exactly, or you may have to simulate the model on a computer -- i.e., let the computer imitate the real system to see what happens as you change some of the parameters.

As usual, the power of mathematics and statistics comes from its ability to handle general abstract problems and then to apply these general methods to an enormous variety of problems.

### Finance

Wall Street has become a major employer of mathstat majors. Trying to match the outstanding success of multibillionaire Differential Geometer, James Simons (founder of the Renaissance Technologies Corporation and the top hedge fund, the Medallion Fund), many investment and financial firms consider mathstat majors prized hires.

### Statistics

Even though you may not have realized it, you probably have made some statistical statements in your everyday conversation or thinking. Statements like "I sleep for about eight hours per night on average" and "You are more likely to pass the exam if you start preparing earlier" are actually statistical in nature.

Statistics is a discipline which is concerned with: designing experiments and other data collection, summarizing information to aid understanding, drawing conclusions from data, and estimating the present or predicting the future. The two statements at the beginning illustrate some of these points.

In making predictions, Statistics uses the companion subject of Probability, which models chance mathematically and enables calculations of chance in complicated cases.

Today, statistics has become an important tool in the work of many academic disciplines such as medicine, psychology, education, sociology, engineering, and physics, just to name a few. Statistics is also important in many aspects of society such as business, industry, and government. Because of the increasing use of statistics in so many areas of our lives, it has become very desirable to understand and practice statistical thinking. This is important even if you do not use statistical methods directly.

This proliferation of statistics in everything ranging from business to government has induced many organizations to seek mathematics-statistics majors.  Statisticians use surveys -- for example, opinion polls -- to predict the patterns of behavior of large groups based on relatively small samples. They ask questions such as: How can we be sure that what we predict from our small sample is true of the population being sampled? Probability theory provides the theoretical foundation for statistics.

One business with an extreme interest in statistics is insurance. The (highly paid) professionals responsible for computing insurance rates are specialist statisticians called actuaries.

### Where MathStat Meets Computer Science

The computer industry provides many lucrative jobs for mathstat majors. Beyond mere proficiency in computer programming, mathstat majors are trained to address the more fundamental issues involved in the creation of new algorithms. Furthermore, many sophisticated applications of computers such as creation of computer graphics and the compression of video and audio signals (to name a few examples) involve a great deal of deep mathematics, and as a result, many computer companies specifically hire math majors.

### Cryptography

One area that is particularly "hot" these days is cryptography - the making and breaking of secret codes. The CIA, NSA, and other spy agencies are not the only devotees. Numerous businesses also require cryptography. For example, the cable TV companies encode their signals, forcing the viewer to rent their decoding devices in order to turn the signals back into a television picture. Banks also employ cryptography in order to protect the privacy and integrity of their transactions. Number theory is the branch of pure mathematics which provides the theoretical underpinnings for much of the recent progress in cryptography.

### Biotech

Recent breakthroughs in the study of  DNA and proteins have generated a great deal of interest in mathematical biology. Many biotech companies hire mathstat majors because of the high (and growing) mathematical content of the field.

### Teaching

If you would like to give back to your community and serve children, teaching at the secondary school level can be very rewarding. Every year, roughly half of the positions advertised for secondary school teachers in math go unfilled. Schools are desperate for qualified mathstat majors.

At the end of your undergraduate years, you may have fallen in love with the beauty of mathematics and want to learn more. You may wish to go to graduate school in mathematics or statistics or a related field (e.g., operation research, economics, computer science, etc.). In graduate school, students typically get paid (albeit not much) to pursue a Master or PhD degree. With a graduate degree, you may find a teaching or research job in academia, or a leadership position in industry.

### Double Major

We would be remiss if we did not discuss double majors. Anyone majoring in any of the STEM fields should seriously consider double majoring with mathstat. Doing so will give you more of the mathematical skills necessary for success in your field. But additionally, a double major in mathstat will cause you to stand out if you decide to apply to graduate school.

### Entrance Exams

And finally suppose you love mathematics, but ultimately see yourself pursuing a career as a doctor, lawyer, or businessman. Then you should be aware that professional graduate schools in business, law, and medicine think mathematics is a great major because it develops analytical skills and the ability to work in a problem solving environment. Their entrance tests support this bias. A study of college students' scores on admission tests for graduate and professional schools showed that students majoring in mathematics received scores substantially higher than the average on each of the tests studied. The study, by the National Institute of Education, compared the scores of 550,000 college students who took the LSAT and GMAT with data collected over the previous eighteen years. The table below excerpts some of this data from The Chronicle of Higher Education. The entries show the percentage by which the mean score of test takers from specific undergraduate majors differs from the mean score of all test takers.

 Major LSAT GMAT Mathstat +12.8% +13.3% Philosophy +8.7% +11.0% Economics +9.6 +7.3 Chemistry +7.6% +7.5% English +5.6% +4.1% Foreign Langs +5.7% +3.3% History +2.9% +4.6% Biology +4.0% +3.3% Psychology +0.9% +0.8% Political Science -1.6% +.06% Arts & Music -.05% -1.2% Business -4.5% -0.8% Sociology -7.0% -5.0% Education -8.7% -4.2%

# Salary Trends in Mathematics and Statistics

In today’s job market, a graduate degree is almost essential for success. And as noted above, a single or double major in mathstat can help you stand out when you apply to graduate school or take the Entrance Exam for a professional graduate program. But even a Bachelor’s degree in mathstat can help you in the job market.

The table below contains data extracted from the National Association of Colleges and Employers 2005 salary survey. It provides a comparison of average starting salaries for students by undergraduate major. Here the base salary is that of an English major.

 Major Salary Differential Mathstat +37.7% Economics +33.5% Chemistry +22.8% Foreign Langs +5.1% Political Science +4.9% History +0.9% Biology +0.8% English +0% Sociology -0.3% Psychology -4.4%

In addition to higher pay, a mathstat major's employment promises higher levels of job satisfaction. JobsRated.com ranks 200 jobs according to environment, income, outlook, physical demands, and stress.  Based on these criteria, The top three spots are "Mathematician",  "Actuary", and "Statistician" -- outranking jobs in medicine, finance, engineering, and law.

# High School Preparation

Students who wish to major in mathstat should take college-prep mathematics courses in their high schools. They are further encouraged to take any AP mathematics courses their high school offers. The University’s Office of Admissions evaluates such matters and handles assigning college credit where appropriate

The University makes use of students’ ACT or SAT scores to determine what course to place a student into. We also offer a Math Placement exam to allow for exceptions. More information about how this works can be found at this departmental page.

# How to Major in Mathematics and Statistics

If you want to major or double-major in math and statistics, you should start with the introductory courses:  in math it is Calculus I  (which is MA 125); in statistics it is either Statistical Reasoning and Applications (which is ST 210) or Applied Probability and Statistics (which is ST 315).

Note that not all students are ready for Calculus I. Some students have to take a PreCalculus course or even a more basic course first, depending on their mathematical background. We make use of students’ ACT or SAT scores to determine what course to place a student into. We also offer a Math Placement exam to allow for exceptions. More information about how this works can be found at this departmental page.

After Calculus I, a math and statistics major will need to take Calculus II, Multivariable Calculus, Linear Algebra, Differential Equations, Regression, and so on. Details on the formal requirements of the major can be found on the University Bulletin.

## Special Programs, Co-ops, Internships

The American Mathematical Society funds summer research programs for undergraduates, known as REU programs. Students are encouraged to apply for them. A student’s advisor can help with the application process.

For students seeking summer jobs and internships, the following links can be helpful:

http://www.energy.gov/jobs/career-opportunities

http://www.krellinst.org/csgf/doe-lab-practicum

http://www.ams.org/profession/employment-services/eims/eims-home

http://www.census.gov/research/opportunities/#intern

https://www.nsa.gov/careers/opportunities_4_u/students/index.shtml

http://nasajobs.nasa.gov/jobs/civil_service_jobs/career/page10.htm

https://www.cia.gov/careers/student-opportunities

http://www.ams.org/programs/students/emp-reu

## Mathematics and Statistics Highlights

The Department has a number of events throughout the year.

• Department Colloquia: these are weekly talks given by World class researchers from around the world. Some of these talks are accessible to advanced undergraduates.
• Mobile Math Circle: this is a weekly event designed for high school students who are interested in mathematics
• Annual Math Competition: this is a contest given in the spring with prizes and scholarships
• Putnam Exam: The William Lowell Putnam Mathematics Competition is a North American math contest for college students. Each year on the first Saturday in December, over 2000 students spend 6 hours (in two sittings) trying to solve 12 problems. The Department runs practice sessions for the exam.

Study abroad is the opportunity for USA students to spend time in a different country while earning credit towards your degree through taking classes, interning, volunteering, and more.  There are many different types of study abroad available to you at USA. They include faculty-led programs, international exchange programs, and direct-enroll and affiliate programs.

Students on faculty-led programs will travel as a group led by USA professors and take classes in various locations. All courses taken on these programs are USA courses and offer USA credits that will apply to your degree. International Exchange programs are partnerships with specific universities around the world with which USA has a special, reciprocal relationship. Students enroll directly at the host university, and students from the host university attend USA. USA affiliate programs allow students to enroll at a partner university or program through a third-party provider. GPA requirements vary by program.

Be sure to visit the OIE Study Abroad website at http://www.southalabama.edu/studyabroad/ to begin your research.  The website contains information on how to get started, financing your program, and a comprehensive list of pre-approved study abroad programs and partners. While researching a passport or visa programs, consider the following: eligibility requirements, location, course offerings, and costs.  You should also meet with your faculty advisor for assistance in selecting a program based on courses related to your degree.

Studying abroad can be one of the highlights of your university career, giving you wonderful and challenging experiences that will allow you to grow both academically and professionally. Where will you study abroad?

To see a sample academic plan for this major, please click here.  Degree plans provide only a suggested schedule; make sure to meet with your academic advisor to find the actual schedule that is right for you.

You can find us on campus at:

Department of Mathematics and Statistics
Instructional Laboratory Building (ILB)
411 University Boulevard North
Mobile, AL 36688
(251) 460-6264