## The Field of Mathematics

Mathematics begins with simple questions in arithmetic. This has led to harder and harder questions involving a huge array of techniques. Perhaps the best way of understanding the scope of mathematics is to look at some examples of questions that mathematicians have worked on and are working on.

A prime number is an integer that cannot be factored into the product of two smaller integers. Every number can be written as the product of primes. Thus primes are the building blocks of the integers. It is easy to tell if you have a prime number, but can you give a method for deciding whether a number, say one with 200 digits, is prime that works quickly? Can you give a method that works quickly for factoring a number into prime factors? These are simple questions, but efforts to answer them have led to much elegant and deep mathematics. And the answers to these questions are useful. Many of the encryption devices we use every day are based on the fact that we can quickly tell if a number is prime and we cannot quickly factor numbers.

Is the planetary system stable? In other words taking into account only gravity will the planets keep revolving around the sun or will they fall into the sun or will they move farther and farther away from the sun? We assume that the sun does not change and that there are no visitors to the planetary system. Efforts to answer this question have led to the study of chaos and fractals.

Diseases sometimes appear in geographical clusters. When do these clusters indicate that the disease is caused by something in the environment near the cluster? More generally one can ask how does exposure to a certain substance effect the probability of an individual developing a certain kind of cancer? Often one can find two explanations that describe a data set equally well. Which is the better explanation? These are examples of a broad array of questions having to do with using imperfect and incomplete data to understand the behavior of complicated systems.

The rapid advance in genetics has led to a plethora of problems that have a large mathematical component. We describe one technique and a pair of problems arising from this technique. A micro-array tells us which genes in an organism are being expressed at a single instant. This tells us roughly what proteins are being manufactured at that time. For example from a single yeast cell we obtain information about the productions of 5,000 kinds of protein. If we repeat this experiment 12 times we seem to have the information needed to get a picture of the biochemical pathways of the organism. This knowledge will help us understand, for example, how undifferentiated stem cells become blood cells or muscle cells, or how diseases harm an organism.

But there are several challenges to overcome. First micro-array readings are prone to noise which could come from tiny differences in the measurement methods or initial conditions (for example ambient temperature). One needs to mathematically model this noise in order to compensate for it. The second challenge is to develop methods of handling the huge amount of data produced by micro-arrays. How does one find patterns in this set of data. This is called data mining. Clearly techniques for analyzing a huge data base can be used in many endeavors - for example ecology.

## Mathematics Majors

The goal of the mathematics program at the University of Massachusetts has three aspects. First the students learn basic material such as linear algebra, differential equations, and statistics needed to successfully attack a wide range of problems. Second, they learn to think with rigor. Lastly they learn to approach apparently unsolvable problems by studying simpler problems, doing experiments and bringing together different concepts.

All majors must complete a calculus sequence and courses in linear algebra, modern algebra and analysis. Each major has wide freedom of choice in upper-division courses and can, with the assistance of a faculty advisor, tailor a program to their interests and career goals. For example, one can prepare for a career in actuarial work, statistical analysis, computer programming, data processing, industry, government, or secondary school teaching. One can also prepare for graduate study in mathematics, statistics, computer science and other fields or professional programs in business, law, medicine and education.

# Actuarial Science

## Introduction

The actuarial field is a vibrant one and a great way to put to use the mathematics and statistics knowledge you are learning as a major. Actuary is listed as the 4th best job in the 2014 U.S. Bureau of Labor Statistics survey behind Mathematician, Tenured Professor, and Statistician.

The Department of Mathematics and Statistics offers several courses to prepare students for an actuarial career, including courses to prepare for the first two actuarial exams, as well as all of the VEE requirements. We are one of only three institutions in Massachusetts on the 2018 UCAP list maintained by the Society of Actuaries.

We currently have about 200 students selecting the Actuarial Concentration within the major, several of whom are also majoring in another field (Finance, Engineering, Economics,...). Our alumni are employed at insurance and other financial companies throughout the country. We host an Actuarial Career Fair each fall and our Actuarial Club holds events throughout the year.

Our Casualty Actuary Society (CAS) University Liaisons are Chad Wilson and Hayley Shi, from Travelers. Chad is a Fellow of the CAS and Hayley is active in the Property and Casualty analytics space and is also a recent UMass graduate.

Thanks to Robert and Lynne Pollack for their generous donations to the program over the past several years.

Companies with internship or job opportunities for our students should post their positions on Handshake. They may also contact the Director of Actuarial Program, Jinguo Lian.

## VEE Requirements

The actuarial societies require several courses as part of the process of obtaining certification within the profession. These courses are known as Validation by Educational Experience (VEE). As of July 1, 2018, the areas and courses are:

• Economics: Microeconomics (Economics 103 or Resource Economics 102) and Macroeconomics (Economics 104)
• Mathematical Statistics: Statistics 515 and 516
• Accounting and Finance: Accounting 221 and Finance 301.

Math majors who have declared the Actuarial concentration may contact Jacob Lagerstrom to submit a request to be enrolled in Accounting 221 or Finance 301. Requests for enrollment should occur during advising week.

## Actuarial Exam Courses

The department offers several courses related to the actuarial exams. Students must take at least one of the exam courses, and also the Math Finance course (Math 537), for the concentration.

Exam P/1: This is an exam covering probability. Math 536 is a course dedicated to preparing students for the exam. The underlying material is covered in Stat 515 and Math 233 and a few students have taken the exam after completing just those courses by studying on their own.

Exam FM/2: The updated version of this exam covers just the interest rate theory material. Math 437 is dedicated to preparing students for this exam. Some of the material is also touched upon in Finance 301.

IFM/3: Math 537 covers a portion of the subject matter of this exam, but 537 is not an exam preparation course per se. Some topics are covered in Finance 301.

Exam SRM (Statistics for Risk Modeling): This is one of the two components of the new curriculum that is devoted to predictive analytics education. It provides the transition from mathematical statistics as presented in the Probability Exam and Mathematical Statistics VEE to predictive analytics and its applications. It covers the regression and time series topics formerly in the Applied Statistics VEE subject. Stat 525 and Stat 535 will be helpful preparation for this exam.

## Suggestions and announcements for actuarial concentrators

• Complete Stat 515 in your sophomore year.
• Take an exam course (typically, Math 536) during your sophomore year so that you can pass one exam by the summer before junior year. This makes it more likely to secure an internship during the Actuarial Career Fair and thus have an internship during the summer between junior and senior year.
• Bob and Lynne Pollack Actuarial Exam Fund: The department will reimburse the full fee for any of the first three exams that are successfully passed. In addition, for students who fail the exam for the first time, the department will reimburse part of the cost of study materials. You may get all of materials (receipt of exam registration, receipt of textbook, exam pass (or not pass) certificate, a thank you letter to Bob and Lynne Pollack) ready before you contact the Director of the Actuarial Program, Jinguo Lian for more details.
• The Actuarial club is a chapter of Gamma Iota Sigma, a national organization of students interested in risk and insurance (including actuarial science).

# Career Opportunities for Mathematics Majors

#### Recommendations

Graduate School: Approximately 30% of recent graduates immediately enroll in graduate programs. Of those students who entered grad school from the classes of 2020 and 2021, 77% enrolled in Master’s programs; 23% enrolled directly in Doctoral programs. They are attending institutions including:

• UMass Amherst
• Northeastern
• UC Berkeley
• McGill
• Duke
• Brown
• Boston University
• Johns Hopkins University

Some of the programs our graduates have recently gone on to study include:

• Mathematics / Applied Mathematics
• Biostatistics / Statistics / Applied Statistics
• Computer Science
• Physics
• Data Science / Data Analytics
• Finance / Economics / Business Analytics
• Education (K-12)

Employment: For the Class of 2021, the most common jobs were in data and analytics, research, actuarial services, finance and business management, and education. Top employers of our majors in recent years include:

• Financial / Insurance Services: Liberty Mutual, MassMutual, Hanover Insurance, Amica
• Government / Defense: General Dynamics, McLaughlin Research Corporation, Federal Reserve Board, US Air Force
• Internet / Software / Telecommunications: Amazon, Oracle, National Grid, Microsoft
• Education: Teach for America, Public Higher Education Network of Massachusetts, Boston Public Schools
• Research: Underwriters Laboratories (UL), MIT Lincoln Laboratory, Broad Institute, UMass Amherst
• An interesting example, and likely our highest paid recent major, is Andy Isabella, who was a second round NFL draft pick in 2019 and plays for the Arizona Cardinals

Class of 2021 job titles include:

• Technical Analyst
• Associate Solution Analyst
• Actuarial Analyst
• Enterprise Data Modeler
• Technical Solutions Engineer
• Marketing Data Analyst
• Bioinformatics Engineer
• Associate Data Engineer
• Quality Systems Associate
• Research Associate

### Internships

Students in the Department of Mathematics and Statistics are encouraged to pursue an internship or research experience as an undergraduate student. Internships provide practical job experience and allow students to gain experience interviewing and network with professionals in the field. Students who are interested in a summer REU (research experience for undergraduates) may apply for the UMass Math REU or search for opportunities at other sites. To search for industry internships, undergraduate students are encouraged to utilize Handshake or speak with a career advisor in the department or in the CNS Career and Professional Development Center. For a list of internships our students have completed in past years, click here.

### Departmental Career Events

Each semester the department hosts career events aimed at undergraduate math majors. Recent programs include:

Spring 2020:

• Anthony Rentsch, Class of 2018, visited in February and spoke about his graduate work in data science at Harvard and about entering the data science field.  As an undergraduate, Anthony completed his senior thesis on applying statistical techniques in political science, his second major.
• Emily Dwizil, Class of 2019, joined us by Zoom in April and talked about her experiences as a Junior Data Scientist at MassMutual.
• Luis Serrano, a Math PhD working as Content Lead of Artificial Intelligence at Udacity, will joined us by Zoom to talk about machine learning and opportunities for majors in industry.

Fall 2019:

• Melissa Campbell, Class of 2018, visited us from Optum, a unit of United Health Care.  Melissa shared her experience of working as a Python programmer and software engineer.

### Employers

Are you an employer interested in hiring our students? To reach our undergrads, there are two ways: you can email the Chief Undergraduate Advisor or post your job to Handshake.

### Career Services

All students should join Handshake, which contains job and internship opportunities for UMass students and alumni.

UMass Career Resources:

Professional Organizations & Job Boards:

Internships and REUs

### General Recommendations for all Career Paths

In the past half century there has been a great increase in the importance of mathematics to our society. The need for trained mathematicians at all levels is on the rise as the use of computers and automation has spread to almost all sectors of our economy. Nowadays, technological, engineering and business problems are often of such complexity that they require a high level of mathematical treatment. Whereas in the past advanced mathematics was generally restricted to the physical sciences and engineering, today there is an ever growing demand for mathematical expertise in the biological and social sciences, as well as in finance and business management and the burgeoning field of data science.

Every student should carefully consider the following five points when deciding on a course of studies during the undergraduate major.

1. A balanced set of core courses in mathematics and statistics.

Of course, many of those courses will be determined by the major concentration, which in turn depends on the intended career path. But every student should be sure to take a good balance of courses. Especially, there should be some mix of mathematics with statistics, and of theoretical and pure courses with applied courses. This kind of balance is really crucial for those students who will pursue work in the non-academic world, and for students who intend to undertake interdisciplinary graduate studies. Even students who plan to enroll in graduate studies in mathematics or statistics, or will train to be secondary school teachers, should make sure that they have sufficient breadth at the undergraduate level in order to take full advantage of their later studies.

2. An extensive exposure to computing.

One of the main reasons that mathematics and statistics are of such importance in the modern world is that they are so closely allied with computation of all sorts. In virtually every profession based on mathematical or statistical knowledge, computing plays a key role. For this reason, students should take enough courses in computer science, scientific computing or information technology to gain expertise with computational techniques and platforms.

3. Some coherent studies in another related field.

It is highly desirable for a student to develop a base of knowledge in another field related to mathematics or statistics. For instance, a successful career might be built on a mathematics major together with a minor in computer science, finance, economics, physics, chemistry, biology, public health or a branch of engineering. If a minor is not feasible, then it is advisable to take a few related courses that complement the studies in the major.

4. An array of "soft" skills.

Mathematics and statistics are "hard" sciences in the sense that their subject matter is technical and abstract. Consequently, their usefulness and relevance to the world is hugely dependent upon how well mathematicians and statisticians relate to their colleagues and coworkers. Employers often talk about how it is absolutely necessary for their technical staff to be able to communicate in writing and orally, to interact productively in teams and groups, and to be diligent, versatile and innovative. These people skills are equally necessary in the teaching professions. A good selection of General Education courses and other electives is one way to develop these skills, as are independent studies and projects, extracurricular activities and even hobbies.

5. An internship, coop or summer research experience.

One of the best ways to procure a good job upon graduation is to have done an internship or coop beforehand. Employers like to have a chance to see a student in the actual work environment, and the student benefits by trying out the kind of work that the employer offers. For students considering graduate study, it is highly desirable to apply for summer Research Experience for Undergraduates (REU) either at your home university or at sites elsewhere in the country. See the links on this page to the university offices on campus that coordinate internships and coops, and to the NSF, NSA and other agencies that offer summer research experiences.

### Specific Recommendations Within the Career Categories

#### Actuarial Science

Actuaries are business executives who use mathematical and statistical skills to define, analyze, and solve complex problems arising in the insurance and pension fields. They create and manage programs to reduce the financial impact of events such as illness, accidents, unemployment, or premature death. Actuaries must understand the entire operation of the insurance and pension fields because their evaluations often influence company policies and practices. Besides good command financial markets, tax and insurance law, regulatory requirements, accounting, and so forth, an actuary must have solid background in applied mathematics and statistics.

Professional status is attained through fellowship in one of two actuarial societies (CAS or SOA). Fellowship is earned, and most of the theoretical training is provided, by passing a series of rigorous examinations sponsored by the societies.   Please see our departmental Actuarial Program webpage.

#### Data Science

In the last few years, the field of data science has exploded.  Majors who have taken Stat 525 (Linear Regression) and have profiency in SAS, R, or Python are particularly well-poised to take advantage of these opportunites.  Students are encouraged to enhance their data science credentials by combining statistical coursework in our department with data science or machine learning coursework in Computer Science, Biostats, or Linguistics.  The following site has extensive information on the field of data science:  Masters in Data Science.  The MassMutual Data Center in downtown Amherst is becoming a vital player in training our students and providing them employment.  Seniors are encouraged to apply to the MassMutual Data Science Development Program

#### Information Technology and Computing

A mathematics major can launch a career in the wide-ranging world of information technology and computing services, provided that the major studies are complemented by enough training in computer science. Typically, such a major will also complete a minor, or perhaps a double major, in computer science. Some of the more mathematically intensive parts of IT concern cryptography or animation and graphics. There are also many positions as applications programmers, that is computer programmers who tailor algorithms to fit the specific needs of clients and companies. Other occupations in this area include network management, web development, security systems, and mobile computing.

Successful completion of a major in mathematics and a minor in computer science is also good preparation for a graduate program in Computer Science. A Master's degree in this computer science is beneficial for some of the more challenging and innovative opportunities. Further information is available from the Association of Computing Machinery:
https://jobs.acm.org/

There is an increasing demand for mathematicians and statisticians in many different areas of business. Besides the clearly defined career path to actuarial science, there are also diverse opportunities in production management, forecasting and financial modeling. A major in mathematics that includes statistics, augmented by a minor in computer science and courses in economics, accounting, finance, or industrial engineering, for example, would provide a solid basis for a business career.

Almost all the positions in this broad range of vocations are advertised with titles that do not include the words "mathematician" or even "statistician." Normally, the positions are for "analysts" of some kind. In recent years there have been burgeoning opportunities in the area of quantitative financial analysis, the practitioners being referred to as "quants." This work focuses on stock market analysis, risk management, financial derivatives and related products. While a bachelor's degree is sufficient for entry into the field, there is also a strong demand for employees with more training. For instance, there are many Master's degree program in Financial Mathematics, and Ph.D.s in the mathematical sciences are often engaged in work in this field. Some of the many resources on the web include:

The problem solving and critical thinking skills possessed by mathematics and statistics majors make them very desirable candidates for positions with consulting firms. These positions are accessible with a bachelor's degree, but they require a quick and adept mind that combines quantitative expertise with business acumen and excellent communication skills. A web search for "quantitative consulting" yields numerous opportunities in this direction.

A mathematics major who wishes to prepare for a career in a government agency would do well to focus on statistics and applied mathematics and to complete a minor in computer science.

#### Teaching at elementary or secondary school level

There is a continuing demand for qualified mathematics teachers in the nation's secondary schools. Besides training in their major field, future teachers must also complete state certification requirements. Most of the information here is for students who wish to teach in secondary schools. Students who wish to teach in elementary school take Mathematics For Elementary School Teachers I and II (Math 113 and 114). School districts across the country are increasingly in need of mathematics specialists in elementary schools. Mathematics majors who are interested in elementary education should consider the possibility of such a career path. Students are also encouraged to explore teaching mathematics in middle school, where there is very high demand for mathematics majors.

Mathematics majors wishing to obtain the intermediate equivalent of the Massachusetts certification to teach mathematics at the middle or high school level must:

• include courses that satisfy the Commonwealth's Standard I requirements on subject matter knowledge;
• complete the School of Education's Secondary Teacher Education Program;
• achieve a passing score on both sections of the Massachusetts Test for Educator Licensure (MTEL).

Any student who is interested in becoming a middle or high school mathematics teacher should contact the Secondary Teacher Education Program. The program includes student teaching, which requires a full semester during which regular courses cannot be taken. For this reason, these students should plan to complete most of their requirements before their student teaching, as they will have one less semester to satisfy Departmental, College, and University requirements.

The Commonwealth's Standard I Subject Matter Knowledge for mathematics states: "The effective teacher of mathematics has completed the college's or university's requirements for a major in mathematics, or the equivalent, by demonstrating knowledge of: mathematics, including: algebra, geometry, analytical geometry, trigonometry, calculus, number theory, probability and statistics, and the history of mathematics; how to use computers in mathematics; modes of inquiry and methods of research in mathematics; relationships between mathematics and other fields of knowledge."

The teaching concentration is designed to help the student fulfill these requirements. Further details are available at

The following courses can be used to satisfy the Commonwealth requirements:

• algebra, analytical geometry, trigonometry, calculus: Math 233
• geometry: Math 461, Math 563
• number theory:  Math 471
• probability and statistics: Stat 501, Stat 515
• history of mathematics:  Math 475
• discrete mathematics:  Math 455
• abstract algebra:  Math 411 or Math 490A
• how to use computers in mathematics: Math 471 (Math 551 is also an option)
• modes of inquiry and methods of research: Math 300, Math 411, Math 456, Math 523
• relationships between mathematics and other fields:  Physics 151-153 or 171-173, Math 331, Math 456, Math 532, Math 534, Math 545.

The Department of Mathematics & Statistics is in the process of developing courses specifically geared to future secondary mathematics teachers, especially in light of the Common Core State Standards in Mathematics (http://www.corestandards.org) and in light of the recommendations of The Education of Mathematics Teachers I and II, Conference Board of the Mathematical Sciences, published by the American Math Society, 2001 and 2012 (available from http://cbmsweb.org/MET_Document/). For instance, on an experimental basis, we offer Math 597T Mathematical Knowledge for Teaching I. Students interested in a teaching career are encouraged to take this course.

Completion of the School of Education's Secondary Teacher Education Program for Prospective Middle and High School Teachers of Mathematics requires the following courses: Students may enroll in (1)-(3) prior to applying to STEP; to enroll in (4)-(7) the student must already be in STEP.

1. Educ 524: Work of the Middle and High School Teacher
2. Psych 305: Educational Psychology, Psych 355: Adolescent Psychology or Educ 693I: Psychology in the Classroom
3. Educ 497I: Tutoring in Schools (or an alternative course option)
4. Educ 592S: Pre-Practicum
5. Educ 511: Teaching Mathematics in Middle and High School
6. Educ 510: The Teacher in the Classroom and Educ 615J: Education and the Law (Taken while student teaching)
7. Educ 500M (503): Student Teaching (5-9) or Educ 500S (504): Student Teaching (9-l2) or both for 5-12 certification.

There are three main options for graduate study following a undergraduate degree in mathematics or statistics. Students are advised to consult departmental faculty about these options as well as the attributes of particular graduate programs nationwide.

Every major research university has a graduate program in mathematics, and the majority are primarily focused on the Ph.D. Many universities have separate departments and Ph.D. programs in statistics, biostatistics and related quantitative areas. The doctoral graduates from these programs find employment either in academic institutions or else pursue careers in government, business, or industry.

There are about 1500 colleges and universities in the United States, which seek to fill their faculty positions with Ph.D.-qualified candidates. These positions involve a mixture of teaching, research and service responsibilities. The particular blend of these activities varies with the type of academic institution (research university, liberal arts college, etc.). This job market tends to be quite tight and there is strong competition for the most desirable opportunities. Those who go into graduate programs intending to teach at the college level should strive to acquire a broad foundation in both theoretical and applied subjects in the field, along with some experience in communicating the subject matter.

2. A professional Master's degree program in applied mathematics or statistics.

An alternative to the traditional Ph.D.-oriented graduate program is a terminal Master's program, which is now available at an increasing number of universities. These programs tend to be in either applied mathematics or statistics. Normally they grant the Master's degree after two years of study. Upon graduation students are qualified to take competitive positions in industry, business or government. Such a program can also be used as a bridge for a student who intends to do a Ph.D. in mathematics or statistics, a Ph.D. in a field other than mathematics and statistics, or an interdisciplinary Ph.D. One of the longest running Masters in Applied Mathematics programs is here at the University of Massachusetts Amherst; see http://www.math.umass.edu/Grad/appliedms.html. In addition, our Department offers a Masters degree with an option in Statistics; see http://www.math.umass.edu/Grad/Stat/stat.html.

3. A graduate program in an interdisciplinary field that is allied with mathematics or statistics.

Yet another pathway is to graduate-level studies in a field that is related to mathematics or statistics. Students pursuing this path will have undertaken a broad program at the undergraduate level, probably having completed a minor or double major in the other field. Examples include physics, computer science, engineering, mathematical finance, biostatistics, bioinformatics, mathematical biology, or operations research. In addition, it is possible to undertake a professional degree in law or medicine after an undergraduate degree in mathematics or statistics.

Talented students who intend to pursue postgraduate studies should also consider participating in the Mathematics Honors Program. Also, graduate courses are open to undergraduates with the consent of the instructor, and majors may wish to enroll in beginning graduate courses, especially those at the 600-level.

# Course Offerings

## Lower-division Mathematics Courses

Course Title Offered
Math 131 Calculus I Fall/Spring/Summer
Math 131H Calculus I (honors) Fall
Math 132 Calculus II Fall/Spring/Summer
Math 132H Calculus II (honors) Fall
Math 196 Independent Study By arrangement
Math 233 Multivariable Calculus Fall/Spring/Summer
Math 233H Multivariable Calculus (Honors) Fall
Math 235 Introduction to Linear Algebra Fall/Spring/Summer
Math 235H Introduction to Linear Algebra (Honors) Fall
Math 296 Independent Study By arrangement
Math 300 Fundamental Concepts of Mathematics Fall/Spring
Math 370 Writing in Mathematics Fall/Spring
Stat 108 Foundations of Data Science Spring
Stat 111 Elementary Statistics Fall/Spring
Stat 240 Intro to Statistics Fall/Spring/Summer

## Upper-division Mathematics Courses

Course Title Offered
Math 331 Ordinary Differential Equations Fall/Spring/Summer
Math 396 Independent Study By arrangement
Math 397C ST - Mathematical Computing Irregular
Math 411 Introduction to Abstract Algebra I Fall/Spring
Math 412 Introduction to Abstract Algebra II Spring
Math 421 Complex Variables Fall/Spring
Math 437 Actuarial Financial Math Fall
Math 455 Introduction to Discrete Structures Fall/Spring
Math 456 Mathematical Modeling Fall/Spring
Math 461 Affine and Projective Geometry I Fall
Math 462 Affine and Projective Geometry II Irregular
Math 471 Theory of Numbers Fall/Spring
Math 475 History of Mathematics Spring
Math 491A Problem Solving Seminar Fall
Math 496 Independent Study By arrangement
Math 497K ST - Knot Theory Irregular
Math 499C Capstone Course I Fall
Math 499D Capstone Course II Spring
Math 499T Honors Thesis By arrangement
Math 499Y Honors Research By arrangement
Math 513 Combinatorics Irregular
Math 523H Introduction to Modern Analysis Fall/Spring
Math 524 Introduction to Modern Analysis II Spring
Math 532H Nonlinear Dynamics & Chaos with Applications Fall
Math 534H Introduction to Partial Differential Equations Spring
Math 536 Mathematical Foundations of Actuarial Science Spring
Math 537 Introduction to Mathematics of Finance Fall/Spring
Math 545 Linear Algebra for Applied Mathematics Fall/Spring
Math 551 Numerical Analysis I Fall/Spring
Math 552 Numerical Analysis II Spring
Math 557 Linear Optimization & Polytopes Irregular
Math 563H Introduction to Differential Geometry Spring
Math 571 Introduction to Math Cryptography Irregular
Math 596 Independent Study By arrangement
Math 597F ST - Fourier Methods Irregular
Stat 310 Fundamental Concepts of Statistics Fall/Spring
Stat 496 Independent Study By arrangement
Stat 499T Honors Thesis By arrangement
Stat 499Y Honors Research By arrangement
Stat 501 Methods of Applied Statistics Fall/Spring
Stat 515 Introduction to Statistics I Fall/Spring
Stat 516 Introduction to Statistics II Fall/Spring
Stat 525 Regressions and Analysis of Variance Fall/Spring
Stat 526 Design of Experiments Every other Spring
Stat 535 Statistical Computing Fall/ sometimes Spring
Stat 596 Independent Study By arrangement

# Honors

## Commonwealth College Honors for Mathematics Majors

Are both commonwealth college honors and departmental honors offered?

Mathematics majors who are also students in Commonwealth College may pursue honors through any of the three standard tracks: Commonwealth College Honors, Commonwealth College Departmental Honors, or Commonwealth College Multidisciplinary Honors. Mathematics majors who satisfy the requirements may also enter Commonwealth College after enrolling in the University.

## Honors Courses

The Department of Mathematics and Statistics offers several honors courses at all levels. All qualified students are encouraged to consider these courses; however, only Commonwealth College students directly benefit from the honors designation.

Course Title Offered Requirements Satisfied
Math 127H Calculus for the Life and Social Sciences I Fall
Math 128H Calculus for the Life and Social Sciences II Spring GenEd: R2
Math 131H Calculus I Fall GenEd: R2
Math 132H Calculus II Fall GenEd: R2
Math 233H Multivariable Calculus Fall/Spring GenEd: R2
Math 235H Linear Algebra Fall GenEd: R2
Math 499C Capstone Course I Not offered CE I
Math 499D Capstone Course II Not offered CE II
Math 511H Abstract Algebra I Not offered
Math 512H Abstract Algebra II Not offered
Math 523H Introduction to Modern Analysis Fall/Spring
Math 532H Topics in Ordinary Differential Equations Fall
Math 534H Introduction to Partial Differential Equations Spring
Math 563H Differential Geometry Spring
Stat 515H Introduction to Statistics I Not offered

With the approval of the Honors Coordinator, students may also receive Honors credit for the following types of courses (subject to the Commonwealth College enrollment cap of 25 students):

• 600/700/800-level courses
• 500-level courses
• Honors independent study courses

Under exceptional circumstances, and with the prior approval of both the instructor and the Honors Coordinator, students may also arrange to obtain honors credit for a 400-level course by adding an Honors Colloquium.

## Departmental Honors

To graduate with Departmental Honors, a student must complete the Mathematics Major with a GPA of at least 3.400 and complete the following courses with grades of B of higher.

1. ENGLWRIT 112H - Honors College Writing. If College Writing is completed prior to CHC admission, a GenEd Honors course (3+ credits) can substitute
2. HONORS 201H - Ideas that Changed the World (Gen Ed "I + US-DU", 4 credits)
3. HONORS 391AH - Special Topics (1 credit)
4. Gen Ed Honors Course (3+ credits)
5. Gen Ed Honors Course (3+ credits). Students may petition to substitute a non-gen Ed Honors Course, please see a CHC advisor for details.
6. One Math/Stat Honors Courses at 400-level or higher
7. A second Math/Stat Honors Courses at 400-level or higher
8. Math/Stat 499Y Honors Research
9. Math/Stat 499T Honors Thesis

Information on Latin Honors can be found at https://www.umass.edu/registrar/students/diploma-and-graduation/latin-ho...

In order to enroll in Departmental Honors, a student must submit a change of major form, signed by the Honors Coordinator, to the registrar.

# Math Competition

## The 36th & 37th Annual Jacob-Cohen-Killam Mathematics Competition

The department held the Jacob-Cohen-Killam Mathematics Competition exam on Tuesday, April 19th from 7-9pm in 151 and 152 Goessmann.

Because of the pandemic, this year the (36th & 37th annual) J-C-K competition was open to all 1st, 2nd & 3rd year degree students at UMass Amherst.

 First Prize \$1600 Second Prize \$1000 Third Prize \$600 Fourth Prize \$200

Prize Winners:

• Bingheng Yang, first [\$1600]

• Chieh-Hui Cheng, second [\$1000]

• Cameron Hurley, third (tie) [\$400]

• Ceilidh Scott, third (tie) [\$400]

Honorable Mentions:

• Pranav Hari [\$125]

• Steven Rossi [\$125]

• Justin Steinmann [\$125]

Continuing Education Students and close relatives of faculty members of the Department of Mathematics & Statistics are not eligible.

 John Baillieul James Francis Roy Perdue

## Past winners

 2004 Elena Zaurova (First Place), Kevin Grimaldi (Second Place), Edward Slavich (Third Place), Thomas Folz-Donahue, Vitaliy Lvin and Michael Sindelar (Honorable Mention) 2005 Kevin Grimaldi (First Place), Shaohan Hu (Second Place), Daniel Arpino (Third Place), Jesse Winn (Honorable Mention) 2006 Shaohan Hu (First Place), Michael Krainin (Second Place), Hilary Scheintaub (Third Place), Alexander McAvoy (Honorable Mention) 2007 Michael Kranin (First Place), Andrew Hall, Kai Xiao (Second Place) 2008 Andrew Hall (First Place), Kai Xiao (Second Place), Kim Kyungyoon (Third Place), Yi Ding (Honorable Mention) 2009 Nathan Harmon (First Place), Keaton Burns (Second Place), Boxuan Cui (Third Place), Anton Medvedev (Fourth Place), Jinlong Tan (Honorable Mention) 2010 Nathan Harmon (First Place), Jingyu Chen (Second Place), Magnum Lew (Third Place), Nicolas Reyes (Fourth Place), Thomas Ryabin (Honorable Mention) 2011 Jingyu Chen (First Place), Sunjeong Im (Second Place), Magnum Lew (Third Place-tied), Keenan Mahan (Third Place-tied), Nicholas Reyes (Honorable Mention), Sofya Vorotnikova (Honorable Mention) 2012 Michael Bjorge (First Place), Andrey Smirnov (First Place), Andrew Maurer (Third Place), Keenan Mahan (Fourth Place), Dan Phelps (Fourth Place), Ryan Szeto (Fourth Place) 2013 Michael Bjorge (First Place), Andrey Smirnov (Second Place), Jeffrey Amirault (Third Place), Ping Fung (Third Place), Nathaniel Scholnick (Third Place) 2014 Batkhuyag Batsaikhan (First Place), Aaron Dunbrack (Second Place), Da Lu (Second Place), Jeremiah Davis (Fourth Place) 2015 Aaron Dunbrack (First Place), Michael Mueller (Second Place), Robert Ambrose (Third Place), Kai Nakamura (Fourth Place) 2016 Thomas Bogue (First Place), Kai Nakamura (First Place), Aubrey Wiederin (First Place - 3-way tie), James Hagborg (Second Place) 2017 James Hagborg (First Place), Alexander Fischer (Second Place), Artem Vysogorets (Third Place), Daniel Weber (Fourth Place) 2018 Patrick Lei (First Place), Nishad Ranade (Second Place), Mark Xiang (Third Place), Shirui Cao (Third Place) 2019 Patrick Lei (First Place), Guanghao Wei (Second Place), Sattwik Das (Third Place), Shirui Cao (Fourth Place), Risen Luan (Fourth Place) 2020 Pranav Garg (First Place), Guanghao Wei (Second Place), Kirin Sarangkasari (Third Place), Dhruba Basu (Fourth Place), Joshua Bornstein (Fourth Place), Stuart Lustig (Fourth Place), Matthew Miller (Fourth Place)

# Minor, Secondary Major, Dual Degree

## Minoring in mathematics

The requirements for the minor in mathematics are the following:

No course used to satisfy the minor requirements may be taken pass/fail.  All courses must be passed.  A cumulative GPA of at least 2.00 in all Mathematics and Statistics courses taken is required.

2. Calculus & Linear Algebra

Math 131, Math 132, Math 233, and Math 235

3. Computer Science

Proficiency in a computer programming language satisfied by CS 121, CS 187, ECE 122, ECE 242, Info 190S or equivalent.  Classes using Matlab are generally not permitted.  Instead, we are looking for serious exposure to programming paradigms and techniques involving a low-level language such as Java, C, C++, or Python.

4. Upper-division Courses

Four upper-division courses of at least 3 credits each.  At most one of these courses may be taken outside of a mathematics and statistics department.  Any course taken in another department must be approved by the Chief Undergraduate Advisor.  At least two of these courses must be taken at UMass.

### Choice of upper-division courses for the minor

Generally, the department expects minors to master material in mathematics and statistics through coursework not required by the major, although at the moment there is no restriction on using coursework to satisfy both the major and the minor.  Students pursuing the minor must take at least three of the four upper-division courses in a mathematics and statistics department.  One and only one course may be from another department, if the course uses mathematics or statistics in a serious way.  See below for a list of courses which require no further approval.

#### Examples:

• An economics major takes Math 331, Stat 515, Math 537, and uses Econ 309 or 452;
• A resource econ major takes Stat 515, Stat 516, Math 537 and uses ResEcon 313;
• A computer science major takes Stat 515, Math 411, Math 471 and uses CS 311 or CS 501;
• An ECE major takes Math 331, Math 421, Math 551 and uses ECE 313;
• An ECE major takes Math 331, Math 425, Math 534H and uses ECE 333;
• A chemistry major takes Math 331, Math 425, Math 461 and then uses Chem 476;
• A physics major makes sure to take CS 121 and then takes Math 331, Stat 515, Math 421 or 563H and then uses Physics 423 or 568;
• An MIE major makes sure to take CS 121 and then takes Math 331, Math 537 (using MIE 273 to satisfy the probability prerequisite), Math 551 and then uses MIE 379.

### Registering for the math minor

If you are interested in registering for the minor, or if you have questions about the minor, please either fill out the course worksheet, email Garret Cahill, or stop by his advising hours, found on our Advising website.

After you register for the minor, you will see your minor listed in your Spire Student Center, below your major.  Once registered, as long as the one and only one course from outside the department is drawn from the Approved Outside Course list, no further action needs to be taken.

If permission is needed to substitute a required course, you should write to Garret Cahill or stop by his advising hours to get approval before you enroll in the course.   Other questions about the minor should also be directed to Garret Cahill.

## Secondary Major

As with any second major, students wishing to obtain a second major in mathematics (SM-Math) need only complete the Junior Year Writing requirement and the Integrative Experience requirement in their primary major.  Secondary majors may use up to two courses from outside the mathematics and statistics department to fulfill open electives in their concentration course requirements (see Approved Outside Courses). Secondary majors in the Statistics and Data Science concentration: using a 390+ Public Health course to satisfy the Advanced Calculus requirement (Math 425 replacement) will count as one of the two allowed outside courses.

To become a secondary major in math, please have a concentration in mind and schedule an appointment for a meeting with a Math/Stat advisor through Navigate.

## Dual Degree

The dual degree awards two UMass degrees to students who earn 150 credits and meet the requirements of two majors.   To obtain the dual degree in math, students need to have the 150 credits, as well as 60 credits in approved CNS (College of Natural Sciences) courses (see Approved CNS Courses).   Students do not need to take Junior Year Writing in math if they have taken it in another major.   They also do not need to take an IE course in math, although most will take one as part of their requirements.

## Approved upper-division courses for minors and majors:

BME 330, Biog 597GE, BioChem/Chem 471, CICS 397A, CS 311, CS 383, CS 445, CS 501, CS 513, CS 514, CS 532, CS 575, CS 585, CS 589, CS 590OP, Chem 475, Chem 476, Chem 584, Chem 585, Chem Eng 231, Chem Eng 475, CE-Engin 260, Econ 309, Econ 452, ECE 213/313, ECE 214/314, ECE 333, LING 492B , MIE 230, MIE 273, MIE 340, MIE 379, Physics 421, Physics 422, Physics 423, Physics 424, Physics 562, Physics 564, Physics 568, Public Health 390R, Public Health 460, Public Health 490Z, and ResEcon 313.  Other courses may be approved on a case-by-case basis:  contact Matthew Dobson (if you are a math major) or Garret Cahill (if you are math minor).

Note:  If you are pursuing a minor in another department (e.g., Econ or CS), please check their implementation of the multiple credential policy to see if courses you are considering using for both the math major and their minor are eligible to fulfill both requirements simultaneously.

# Miscellaneous Information

## Student Memberships in Professional Organizations

### Student Chapter of the Mathematical Association of America

The Mathematical Association of America is the largest professional organization in the world devoted to mathematics at the college level. Its long-range goals are to promote excellence in the teaching of mathematics, to cultivate mathematical talent, and to enhance public awareness of mathematics. It currently has some 34,000 members, approximately 20% of whom are students.

The Department has a charter student chapter of the MAA and encourages its majors to become members. Among the many valuable benefits enjoyed by student chapter members are a free subscription to Focus (the newsletter of the MAA), career information, help with job placement or graduate applications, contact with the mathematics community, opportunities to meet students with similar interests, and eligibility for travel grants to meetings and special conferences.

Application forms and further information can be obtained from the Undergraduate Office.

### National Council of Teachers of Mathematics

The National Council of Teachers of Mathematics is the largest organization in the world dedicated to the improvement of mathematics education and to the needs of teachers of mathematics. Mathematics majors interested in becoming teachers are encouraged to become student members of NCTM. Members receive subscriptions to the NCTM journal Mathematics Teacher and/or the NCTM journal Arithmetic Teacher, and they receive a newsletter, as well as notices concerning special meetings, workshops, etc.

Application forms and further information can be obtained from the Undergraduate Office.

## Approval of Courses To Be Taken at Other Schools

Students who wish to take courses at other institutions during the summer months or while on leave from the University, either to help them fulfill requirements or to make them eligible for an earlier graduation date, must have their proposed course of study evaluated in advance. Mathematics majors planning to use courses to be taken at other schools to satisfy Departmental graduation requirements must obtain prior approval of these courses from the Chief Undergraduate Advisor.

There are three different prior approval forms:

1. Prior Approval Form

This form is to be used by those students who intend to fulfill degree requirements through the completion of courses at other institutions (including other UMass campuses and the National Student Exchange Program) or through the College Level Examination Program (CLEP). The form requires the approval of the Chief Undergraduate Advisor (for courses to be used to satisfy Departmental graduation requirements), Transfer Affairs (for courses to be used for elective credit and/or to fulfill University General Education requirements), a CASIAC dean (for foreign language courses to be used to satisfy the College of Arts and Sciences' Foreign Language Requirement), and an academic dean (for students on academic probation or suspension).

2. Prior Approval Form for Completing the Senior Year in Absentia

This form is to be used only when the student has accumulated 90 or more credits and intends to complete degree requirements or do any portion of the senior year while not in regular attendance at the University, i.e., by taking courses at other institutions (including other UMass campuses), by taking courses by examination, or by earning CLEP credits. This form requires the approval of the Chief Undergraduate Advisor, an academic dean, and the Office of Transfer Affairs.

3. International Program Prior Approval Forms

Students planning to study abroad must file an International Preliminary Registration/Approval form before they depart for study abroad and a Transfer of International Credit form after they return. Both forms are available in the International Programs Office and require the approval of the Chief Undergraduate Advisor (for courses to be used to satisfy Departmental graduation requirements), a CASIAC dean (for courses used to satisfy College requirements), the Office of Transfer Affairs (for courses to be used for elective credit and/or to fulfill University General Education requirements), and the International Programs Office. In addition, students spending any part of their senior year abroad must file a Prior Approval Form for Completing the Senior Year in Absentia.

# R1 (Tier 1) Basic Math Skills Exemption Test

### The R1 Exemption Exam:

Passing the R1 Exemption Exam allows students to complete the R1 graduation requirement without having to take a course that satisfies it.  If you need to take a course for your major that satisfies the R1, there is no reason to take the R1 Exemption Exam.  You will not get any credits for passing the R1 Exemption Exam.  The math placement exam is a separate exam that does not give you the R1 Exemption.

• There are 20 multiple choice questions.
• To pass you need to have at least 12 correct.
• It is taken online through Blackboard and proctored by a remote proctoring service.  There is no cost to students to take this exam.
• You will need the following items when taking the exam:
• A webcam connected to your computer.
• You will have 75 minutes to take it.
• There is a scientific calculator that is integrated into the exam.
• You may take the R1 Exemption Exam one time per testing window.
• The focus of this exam is to measure knowledge of basic math skills. The Math Department does not provide study materials.  You can use a variety of free online sites to help you study.  Topics include:
• perimeter, area, volume
• linear equations
• averages
• fractions
• ratios
• percent increase and decrease
• interpreting graphs and tables
• compound interest

#### Windows for Upcoming Exams:

The Exemption Exam is given two times a semester. The exam will be open for two days, from 5 am of the first day to 11 pm of the second day.  You may take it anytime within those two days.  If you miss taking it, you will have to sign up again the next time it is offered.  ** All times are EST **

#### Fall 2022 (subject to change with University Academic Calendar)

• Wednesday, September 7 - Thursday, September 8
• Wednesday, December 7 - Thursday, December 8

1. Submit this form.  For the September 7-8 testing window, you must fill this form out by Monday, September 5th at 10:00am ET.  We cannot add anyone after the due date because registration is done through the Registrar's Office.  If you miss this deadline to sign up you will have to wait until the December 2022 test dates.  (We will update this site when we begin accepting December 2022 sign ups.)  We will open the Blackboard course on Tuesday, September 6. To get to the exam you will need to sign into UMass Blackboard using your NetID.  You will see the R1 Exemption Exam "course" in your dashboard.
2. In the “Course”, you will see two areas “Practice Exam” and “R1 Exemption Exam”.  In the practice exam area, you will see instructions on how online proctoring works and what you need to do to prepare for the exam.  You can also take the Practice Exam which will allow you to make sure everything will work for you.  Once the exam window is open, you can go to take the exam when you want in the “R1 Exemption Exam” section.
3. You must be an active, currently enrolled student at UMass - Amherst for the semester in which you take the exam at the time you sign up for and take the exam.

#### Exam Results:

You will see whether you passed the exam right after you submit it.  Remember, you need 12 out of 20 correct to pass it.  If you pass the exam you will see this reflected on your SPIRE account within a week.  If you do not pass the exam, you may take it again the next time we offer it, or you can take a course that will satisfy the R1.

#### Questions?

General questions or concerns about accessing the R1 Exemption Exam should be sent to Eric Sarfo Amponsah (esarfoampons@umass.edu), Math Department Lecturer.

If you are having issues with Blackboard, contact elearning@uww.umass.edu or 24/7: https://supportcenter.embanet.com/uma. Honorlock proctoring support can be found at: https://honorlock.com/support/.

UWW students with UWW related questions about the R1 Exemption Exam should contact Shekhar Regmi, (sregmi@uww.umass.edu), UWW R1 Advisor.

#### Summer Research at UMass

The department has its own Summer Research Program supported by gifts to the department and grants to individual professors: Research Experience for Undergraduates at UMass.  Students accepted into the program typically work with individual professors on a project.  Summer 2020 applications are due on March 10.

#### National REU programs

Students who are US citizens or permanent residents are encouraged to apply to one of the national REU programs in the mathematical sciences.

#### Independent Studies

It's also possible work with faculty during the semester on a research project.  This could be informal, or part of an independent study, or as the basis for an Honors Thesis.

# The Math Major and its Requirements

## Introduction

The mathematics degree at UMass provides the student with broad exposure to the most important themes in mathematics and statistics, while allowing the student to specialize in one or more areas. Our rigorous mathematical and statistical training, coupled with exposure to computing paradigms (whether in Java, Python, MATLAB, R, and/or SAS), has provided our majors with increasing success in the job and graduate school marketplace.

In recent years, primary math majors have taken jobs at companies ranging from British Aerospace to Raytheon to Microsoft to Optum to MassMutual to Willis Towers Watson, have begun Master's programs including at WPI, Columbia, Northeastern, and Harvard in a range of fields such as Applied Math, Statistics, Biostatistics, Computer Science, Data Science, Actuarial Science, Education and Business, and have started PhD programs at UC Berkeley, Michigan, NYU, UC Santa Barbara, Columbia, and Boston University in Pure Math, Biostatistics, and Statistics.  Our second majors have used the math degree to amplify their training in such subjects as Economics, Physics, Computer Science, Finance, Engineering, Chemistry, Political Science and Psychology.

## Concentrations within the Major

The department offers seven concentrations as part of the mathematics degree, which allow the student to specialize in one of six focused areas, or create their own:  Actuarial, Applied Math, Individual, Math Computing, Pure Math, Statistics and Data Science, and Teaching.   Students are expected to choose a concentration by the middle of their second semester, but are encouraged to do so earlier.   Please email Jacob Lagerstrom to choose or change your concentration.

## Core Requirements for all Majors

• Differential and integral calculus: Math 131 and 132, with a grade of C or better in Math 132
• Multivariable calculus and linear algebra: Math 233 and 235
• Introduction to abstract mathematics: Math 300 or CompSci 250.  This requirement may be waived by the Chief Undergraduate Advisor, Matthew Dobson, for students who have taken advanced math coursework elsewhere in abstract algebra, real analysis, or number theory.
• Computer programming: CompSci 121 or equivalent
• Writing in mathematics: Math 370
• Integrative Experience (IE) course.  The following courses satisfy the IE requirement:  Math 455, Math 456, Math 475, Stat 525, Stat 494CI.  All IE courses count toward either required major courses or upper level major electives.  In other words, this requirement does not require additional coursework to be completed.
• Completion of the requirements of one of the following concentrations: Actuarial, Applied, Individual, Mathematical Computing, Pure, Statistics and Data Science, Teaching.

• All courses used to satisfy these requirements must be completed with a passing grade (D or higher) and cannot be taken Pass/Fail.
• The overall GPA of all courses taken to satisfy the requirements for the major (averaged over all such courses taken) must be at least 2.0.
• Students will need to earn a grade of C or better in Math 132 before taking certain courses at the 300 level or higher.

## Update on Math 425

Following the Spring 2021 semester, the department will stop offering Math 425.  This course is required for Applied, Pure and Statistics concentrations. See below for the information about which courses can substitute for Math 425.   All replacement courses must be 3 or more credits and cannot be used for another requirement in the concentration.   Also note that we will go into Spire and make the substitution course count; it will not happen automatically.

## Concentrations and their requirements

Mathematics majors must choose one of the following concentrations before registering for their third semester of classes.   Courses from outside the department may be used to satisfy the concentration requirements:  a list of accepted University courses is available here.  The Chief Undergraduate Advisor may approve other courses taken outside the department or at another university, but this must be done before the student enrolls in them.

Note:  If you are pursuing a minor in another department (e.g., Econ or CS), please check their implementation of the multiple credential policy to see if courses you are considering using for both the math major and their minor are eligible to fulfill both requirements simultaneously.

### 1)  Actuarial Concentration

The Actuarial Concentration prepares the student for a career in the actuarial sciences. Requirements:

1. VEE requirements outside the department: Econ 103 (or Res-Econ 102), Econ 104, and Finance 301.
2. Accounting 221 is now a VEE, but it is not yet a requirement of the concentration.  Students are encouraged to take Acct 221.
3. Probability and statistics: Stat 515 and Stat 516
4. Linear Regression:  Stat 525.   Stat 525 is an IE course.
5. Exam preparation: Math 437 or Math 536
6. Mathematics of finance: Math 537
7. Three of the following courses:  Math 331, Math 397C, Math 425, Math 456, Math 523H, Math 545, Math 551, Math 597U, Stat 526, Stat 535, or an appropriate course outside the department such as Finance 422, Econ 309, Econ 452, or Public Health 460.  For other substitutions see the approved outside course list.  Only one course outside the department is permitted.

[Note: The following electives (from item 7) will not count automatically on Spire, and must be requested by the student: Math 397C, Math 597U and any course from the approved outside course list. To request a substitution on Spire, the student must email Jacob Lagerstrom after the course to be substituted is complete and a grade is posted on Spire.]

See the Actuarial Sciences webpage for further details on this concentration.

### 2) Applied Mathematics Concentration

The Applied Mathematics Concentration prepares the student for applied mathematics positions in industry or government. Requirements:

1. Advanced multivariate calculus: Math 425
• The following courses (if not used elsewhere) will substitute for 425:  Math 397C, 421, 523H, 524, 532H, 534H, 552, 597U, Stat 516 or 525
2. Differential equations: Math 331
3. Linear algebra for applied mathematics: Math 545
4. Introduction to scientific computing: Math 551
5. One of the following courses: Math 456, Math 532, Math 534, Math 552.  Math 456 is the IE course for this concentration.
6. Three electives:  three additional Math or Stats courses numbered 400 or higher (except Stat 501)
7. Students are permitted (and encouraged) to take one of the electives outside the department.  Approved courses include MIE 379, Public Health 460, and Econ 309.  For other outside courses see the approved outside course list.

### 3)  Individually Designed Concentration

The individually designed concentration permits students, in consultation with the Chief Undergraduate Advisor, to design their own concentration so as to explore a theme in mathematics or statistics or to investigate connections between the mathematical sciences and another field. An individual concentration includes the core requirements above plus eight courses numbered 400 or above, of at least three credits each.  In practice, very few students choose this option since most of the other concentrations have enough flexibility, including three open electives in both the Applied Math and Statistics and Data Science concentrations.  Generally, the individual concentration will only be approved for students with a single major to allow them to gain exposure to multiple disciplines, rather than as a mechanism to add a second major in math using coursework from a primary major.  Students also have the option to do BDIC if they are interested in a field that utitilizes mathematics, statistics, or data science.

### 4)  Mathematical Computing Concentration

The Mathematical Computing Concentration prepares the student for careers that require both knowledge of advanced mathematics and knowledge of computer science.

Requirements:

1. Data Structures:  CompSci 187 or ECE 242.   This course is needed as a prerequisite to CS 250 (and is also quite useful).
2. Abstract algebra: Math 411
3. Probability: Stat 515
4. Intro Scientific Computing:  Math 551
5. Algorithms: CompSci 311.  (Students who took Math 300, instead of CS 250, will also need to take Math 455)
6. Either CompSci 501, Math 513, or CompSci 575
7. Two additional courses from the following list: Math 331, Math 412, Math 456, Math 471, Math 571Math 545, Math 552, Math 597U or Stat 516. The IE course on this list is Math 456.
8. CS elective:  any 300+ level CS course of 3 credits or more that is not used to satisfy any of the previous requirements.

### 5)  Pure Mathematics Concentration

The Pure Mathematics Concentration gives students exposure to the core mathematics subjects and prepares students for graduate study in mathematics. Requirements:

1. Abstract algebra: Math 411
2. Complex variables: Math 421
3. Real Analysis: Math 523H
4.  Advanced Coursework in Analysis, Geometry or Algebra.  Two courses from Math 425, Math 524, Math 412, Math 497K (Knot Theory), or Math 563H.
5. One applied mathematics course either chosen from the following list or another course with sufficient applied mathematical content approved by the Chief Undergraduate Advisor: Math 331, Math 456, Math 532, Math 534, Math 551, Math 552, Stat 516
6. Two additional courses numbered 400 or higher (except Stat 501). Most students will select one of these to be Math 455 to satisfy the IE requirement. With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department.

### 6)  Statistics and Data Science Concentration

The Statistics and Data Science Concentration prepares the student for a career as a statistician or a data scientist or for graduate study in statistics or biostatistics. Requirements:

1. Advanced multivariate calculus: Math 425
• The following courses (if not used elsewhere) will substitute for 425:  Math 523H or 597U; Stat 310/297F, 526, 535 or any Stat course above 535; Public Health courses at the 390 level or higher (e.g., PH 390R will count).   Replacement courses must be 3 or more credits.
2. Advanced Algebra:  Math 545 or 411
3. Probability and statistics: Stat 515 and Stat 516
4. One of the following courses: Stat 525 or Stat 526.  The IE course on this list is Stat 525.
5. Three electives: three additional Math or Stats courses numbered 400 or higher (or Math 331).  Note: Stat 501 cannot be used for this list.
6. Students are permitted (and encouraged) to take one of the electives outside the department.  Approved courses include Public Health 460 or 490Z, Econ 309 or 452, and MIE 379.  For other approved courses, see the outside course list.

### 7)  Teaching Concentration

The Teaching Concentration provides the student with the knowledge of mathematics and statistics for teaching at the secondary school level.

1. Abstract algebra: Math 411 or 490A
2. Mathematical modeling: Math 331 or Math 456
3. Discrete/finite mathematics: Math 455 (an IE course)
4. Geometry: Math 461
5. Probability and statistics: Stat 501 followed by Stat 515
6. Use of technology: Math 471
7. One additional course numbered 400 or higher.  (Math 475, History of Math, is recommended since it is an education school requirement).

# Transfer and AP Credit and Study Abroad

## Receiving credit or exemption for Calculus I (Math 131)

A student who earns a score of 4 or 5 on the Advanced Placement Calculus AB Exam (or the AB part of the BC Exam) will automatically receive the 4 credits for Math 131 as soon as the registrar receives the exam report from the College Board.   Certain A level and IB exams may also earn the 4 credits for Math 131.   Students must arrange to have their scores sent to UMass.

Starting in Fall 2021, students who need to take Math 131 and who do not have transfer credit for Math 131 or credit from an exam (AP, IB, or A-level) should begin their calculus studies with Math 131.   However, students who feel they have thoroughly mastered the topics of Math 131 through a high school class may take a placement exam during the first week of classes.  The placement exam will satsify requirements for Math 131, but does not lead to credit earned.  See Math 131 Placement Exam information.

For students who completed Math 132 prior to Fall 2021 and earned a grade of C or better on the first try, the 4 credits for Math 131 will be awarded (unless they have already received credit for another Calculus I class).  To receive this credit, the student will need to email Jacob Lagerstrom after receiving the final grade in Math 132.

## Receiving credit for Calculus II (Math 132)

A student who earns a score of 4 or 5 on the Advanced Placement Calculus BC Test will automatically receive the 8 credits for Math 131 and 132, as soon as the registrar receives the exam report from the College Board.  Students must arrange to have their scores sent to UMass.

Prior to 2021, a student who took the IB exam with Higher Level Math(s) with Option 9 (Calculus) and scored a 6 or higher could earn credit for both Math 131 and 132.  If this applies, please send the Mathematics Advising Office an official copy of your IB scores to receive the 4 credits for Math 132.  As of Fall 2021, students taking A levels or IB exams should begin with Math 131 or Math 132, depending on the version of the exam they took.

In summary, the only ways to earn credit for Math 132 are the following: take Math 132 at UMass; take an approved transfer course at another college or university that covers both integration and infinite series; or take the AP BC exam and earn a 4 or 5.   See below for information about Math 132 transfer courses.

## Transfer Credit

• Approval of Courses To Be Taken at Other Universities:  Current students wishing to take a course during the summer months or while on leave from the University at another college or university must complete the Prior Approval form before they enroll in the course and then bring the form to the Mathematics Advising Office.

• Approval of Courses Taken Before Entering the University:  If you are a new student or a transfer student and have taken a math or statistics course elsewhere for which you wish to receive University credit, first make sure the course has transferred over to UMass.  Then, to have it assigned to a specific UMass course, please email the Chief Undergraduate Advisor a link to the course syllabus and send, if possible, a copy of the course's final exam.

• Study Abroad Course Approval:   Students planning to study abroad will need to have courses pre-approved.  The Internation Programs Office will help you get started and then the Chief Undergraduate Advsior, Matthew Dobson, will assist you in filling out the International Course Approval Form (ICAF).

## Approved Transfer Courses for Math 132

Generally, any second course in calculus that is for engineers and math majors, that covers techniques of integration (integration by parts, trig substitution, etc) and that fully covers infinite series (including convergence questions, power series and their convergence, Taylor series) is likely to be approved.  The following courses in MA have already been approved:
Berkshire Cmty College MAT 152
Bristol Cmty College MTH 215
Bunker Hill Cmty College MAT 282
Cape Cod Cmty College MAT 250
Greenfield Cmty College MAT 202
Holyoke Cmty College MTH 114
Massachusetts Bay Cmty College MAT 201
Massasoit Cmty College MATH 222
Middlesex Cmty College (in Mass) MAT 291
Mount Wachusett Cmty College MAT 212
North Shore Cmty College MAT 252
Northern Essex Cmty College MAT 252
Quincy College MAT 206
Quinsigamond Community College MAT 234
Roxbury Cmty College MAT 203 *and* 204
Springfield Tech Cmty College MAT 132
Bridgewater State College MATH 162
Framingham State College MATH 220
Salem State College MAT 221
Univ Mass Boston MATH 141
Univ Mass Dartmouth MATH 152 or 154
Univ Mass Lowell MATH 1320
Westfield State University MATH 106
Worcester State University MA 201

# Tutoring Centers

## Math 131, 132 and 233 Tutoring Center

The Math 131, 132 and 233 Tutoring Center, located in LGRT 140, is a resource for students taking Math 131, Math 132 and Math 233.

Note: The physical location is currently closed. The information for each course is posted below.

Spring 2022

• Math 131: Course-wide tutoring info for Math 131 can be found on each student's Math 131 Moodle page.
• Math 132: Course-wide tutoring info for Math 132 can be found on each student's Math 132 Moodle page.
• Math 233: Course-wide tutoring info for Math 233 can be found on each student's Math 233 Moodle page.

## Math 127 and 128 Tutoring Center

The Math 127 and 128 Tutoring Center, located in LGRT 140, is a resource for students taking Math 127 and 128.

Spring 2022

Note: The physical location is currently closed.

Tutoring information can be found on the Moodle page associated with each course.

## Pre-Calculus Tutoring Center

The Pre-Calculus Tutoring Center, located in LGRT 146, is a resource for students taking Math 100, 101, 102 and 104. The Center is staffed by Undergraduate Teaching Assistants Monday-Friday during the hours listed below.

Spring 2022

Spring 2022 Schedule

## Statistics Tutoring Center

The Statistics Tutoring Center, located in LGRT 170, is a resource for students taking Statistics 240 and 501.

Spring 2022

Note: The physical location is currently closed.

Tutoring information can be found on the Moodle page associated with each course.

Phone: 413-545-2282

Contact Information:

Appointments: Log into Navigate to make an appointment for a meeting (virtual or in-person) with one of the advisors listed above.

In-Person Advising: Appointments can be made through Navigate. Walk-ins will be accepted if there are no appointments, or between appointments.

In LGRT 1521E:

In LGRT 1521C:

In LGRT 1521G:

Becoming a Math Major: First, review the Major requirements and concentrations, then:

All current UMass students must declare a concentration upon entry to the Math major. Existing Majors who entered as Freshmen will be asked to select a concentration before the registration period for their third semester, but are welcome and encouraged to select one earlier. To add or change a concentration, or to select a second concentration, please email Jacob Lagerstrom.

Criteria for Admission to the Major: There are no specific criteria for admission, but Majors should be aware that a C or better is needed in Math 132 in order to take certain upper level courses required for the Major.

Interested in the Minor? Students wishing to minor in math should consult the Minor and Secondary Major page. Direct any questions about the Minor or requests to add the Minor to Garret Cahill.

Undergraduates with appropriate mathematics backgrounds are encouraged to apply for a Teaching Assistantship position. The application deadline for Fall 2022 is May 6, 2022.

### Teaching Assistant (TA) Duties

Below is a list of "typical" duties of Teaching Assistants. Duties will vary for different courses TAs are assigned to assist with. The supervising professor should provide details about expectations for a specific course.

• Assist with the teaching and administration of a large lecture section in a course such as Math 100, 101, 102, 104, 121, 127, 128.
• Attend and assist (with questions, material distribution etc) during the weekly lectures of the supervising professor.
• Prepare and run study groups and discussion sections.
• Hold office hours in the course's help center.
• Serve as proctor in the course's exams.