Mathematical Sciences

• Given a problem, to recognize its mathematical aspects and to produce an abstract mathematical model for the problem.
• Basic mathematical skills (through discrete math, the calculus course, and linear algebra).
• To write mathematics effectively:
  • Math track: To understand and write mathematical proofs.
  • Stats track: To write a professional-level technical report.
• To speak mathematics or statistical terms effectively in oral presentations.
• To use technology appropriately to learn and understand mathematics.

Advisers: Pau Atela, Benjamin Baumer, Jennifer Beichman, Patricia Cahn, Luca Capogna, Christophe Golé, Rajan Mehta, Geremias Polanco, Candice Price, Ileana Streinu, Becca Thomases, Julianna Tymoczko

If you'd like to declare a math major or minor, the first step is to fill out an advisor preference form here.

The mathematics major has a foundation requirement, a core requirement, a depth requirement and a total credit requirement.
 
The foundation requirement consists of MTH 111, MTH 112, MTH 153, MTH 211, and MTH 212. Some of these requirements might be waived for a well-prepared student.
 
The core requirement consists of one course in algebra (MTH 233 or MTH 238) and one course in analysis (MTH 280 or MTH 281). Alternatively, students declaring a math major before Fall '22  may focus on statistics; students pursuing this track through the major are not required to take a course in algebra but instead must complete MTH 220, MTH 246, MTH 320, and either MTH 291 or MTH 290. Students intending to declare a major after Fall '22 do not have this option and are advised to pursue a MST Major (Mathematical Statistics).
 
Majors are required to take at least one advanced course. This is the depth requirement. An advanced course is a mathematics course at Smith numbered between 310 and 390.

• In total, majors must take at least 36 credits among courses numbered at or above 153, with the following exceptions:
• With the approval of the department, up to 8 of the credits may be satisfied by courses taken outside the mathematics and statistics department.
• Courses taken outside the department must contain either substantial mathematical content at a level more advanced than MTH 211 and 212 or statistical content at a level more advanced than MTH 220. Generally, such a 4-credit course will be given 2 credits toward the mathematics major.
• Note that courses that are cross-listed with mathematics and another department (CSC 250, ECO 220, PHI 202, PHI 203, PHI 220, and SDS 292) are counted as mathematics courses and given full credit toward the mathematics major. The following courses meet the criteria for 2 credits toward mathematics major: AST 337, AST 351, AST 352, CHM 331, CHM 332, CSC 240, CSC 252, CSC 274, CSC 334, ECO 240, ECO 255, EGR 220, EGR 315, EGR 320, EGR 326, EGR 374, EGR 389, LOG 100, PHY 210, PHY 317, PHY 318, PHY 319, PHY 327, and SDS 293. A student may petition the department if she wishes credit for any course not on this list.

Normally, all courses that are counted towards either the major or minor must be taken for a letter grade.

The major in mathematical statistics (MST) is designed to prepare students for graduate study in statistics and closely-related disciplines (e.g., biostatistics). The MST major overlaps with the major in Statistical & Data Sciences (SDS), but places a heavier emphasis on the theoretical development of statistics. MST majors will develop sophisticated mathematical skills to prepare for rigorous future study. The MST major also overlaps with the major in Mathematical Sciences (MTH), but focuses on statistics and replaces the algebra requirement with a computing requirement.  

A student majoring in MST cannot have a second major in either SDS or MTH. Students contemplating a double major in MTH and SDS should choose to major in MST. 

Advisers:

1. For an advisor in MTH, please fill out an advisor preference form here
2. For an advisor in SDS, please fill out this form https://bit.ly/sds_advisor

Please see the major requirement diagram.

Requirements

1. Mathematical Foundations (3 courses): The following required courses build foundational mathematical skills.
   • MTH 153: Introduction to Discrete Mathematics
   • MTH 211: Linear Algebra
   • MTH 212: Calculus III
2. Statistical Foundations (2 courses): These courses develop a strong foundation in applied statistics.
   • SDS 201 or SDS 220: Introduction to Statistics
   • SDS 291: Multiple Regression
3. Statistics Depth (1 course): Choose one additional course that provides exposure to additional statistical models.
   • SDS 290: Research Design and Analysis
   • SDS 293: Modeling for Machine Learning
   • SDS 390: Topics in Statistical and Data Sciences
4. Mathematics Depth (1 course): Choose one rigorous course in theoretical mathematics.
   • MTH 280: Advanced Calculus
   • MTH 281: Introduction to Analysis
5. Programming (1 course): Choose one course that provides exposure to computer programming.
   • SDS 192: Introduction to Data Science
   • CSC 110: Introduction to Computer Science
   • CSC 120: Object Oriented Programming
6. Theoretical Statistics (2 courses): A two-course sequence that most directly reflects the graduate school experience.
   • MTH 246: Probability
   • MTH/SDS 320: Mathematical Statistics
7. Electives: (as needed to complete 10 courses): Provided that the requirements listed above are met, other courses may be counted as electives to reach the 10-course requirement. Five College courses in statistics, mathematics, and computer science may be taken as electives. Students should consult with their adviser to determine appropriate electives.

The Minor in Mathematical Sciences

The minor in mathematics consists of 211 and 16 credits taken from among the following: 153, 205 and courses numbered above 211, including two courses above 218. Four of the credits may be replaced by eight credits from the list of approved courses counting for 2 credits towards the MTH major in the description of the major requirements found above.

The Minor in Applied Statistics

The interdepartmental minor in applied statistics offers students a chance to study statistics in the context of a field of application of interest to the student. The minor is designed with enough flexibility to allow a student to choose among many possible fields of application. The minor consists of five courses. Among the courses used to satisfy the student’s major requirement, a maximum of two courses can count towards the minor. Ordinarily, no more than one course graded S/U will be counted towards the minor. See the Statistical & Data Sciences website for more information.

An honors project consists of directed reading, investigation and a thesis. This is an opportunity to engage in scholarship at a high level. A student at any level considering an honors project is encouraged to consult with the director of honors and any member of the department to obtain advice and further information.

Honors projects in the Department of Mathematics & Statistics are worth 8–12 credits. Ideally, your program should be approved by the department in the spring before your senior year. (You might also consider applying for a summer research grant from Smith so you can spend the summer before your senior year in Northampton beginning the work on your project.)

Eligibility

Normally, a student who applies to do honors work must have an overall 3.0 GPA for courses through her junior year, and a 3.3 GPA for courses in her major. A student may apply either in the second semester of her junior year or by the second week of the first semester of her senior year; we strongly recommend the former.

Financial Assistance

The Tomlinson Memorial fund provides financial assistance for honors thesis projects. If you're interested in obtaining funds you must complete the application form "Financial Assistance for Departmental Honors" and submit it with your honors application. This application form can be obtained from the director of honors or the class deans office.

Timeline*

Typically, you meet with your project adviser several times a week. Usually the project focuses on one area and involves reading mathematics papers and books at an advanced level. The honors paper you write will be an assimilation and exposition of the area. Occasionally, a project will include new contributions by the student. By early spring, most of your research should be complete and you will begin writing. The paper is due in the middle of April. It is read by a panel of faculty members, and in early May you present a talk to the department on your work.

Presentation of Thesis

Smith College rules stipulate that the final draft of your thesis must be submitted to your faculty adviser (first reader) and second reader by April 15*. This final draft will be the one subject to evaluation by the first and second readers. Honors candidates give a 45-minute oral presentation of their honors research for the mathematics faculty, which will be open to all interested members of the Smith College community and others by invitation.

You should expect to take questions from the audience during and after the presentation. Following the open presentation there will be an additional question period for the mathematics faculty only. This presentation will be scheduled during the last week of classes, or reading period, but no later than the last day of the pre-examination study period.

Evaluation

• 60% thesis
• 20% oral presentation
• 20% grades in the major

Your grade for the project (pass, distinction, high distinction, highest distinction) is determined by a combination of your grades on the paper, the presentation and your mathematics courses. The presentation has the least weight in your grade, but it gives us all a chance to hear about what you have done. We also invite you to give a talk to your fellow majors, though this is not part of the official process.

*Timeline is for May graduates. Consult your adviser about dates if you plan to graduate in January.

Whatever your reasons to study math or statistics, we, or our colleagues in Statistics & Data Science, have something for you! And by the time you take a course with us, we hope that you will have enjoyed it so much that you will take another one just because it’s cool…

Why do I need math at all?

If you haven’t enjoyed your mathematics courses or have found them frustrating, the need to take more math in college for your major can be irritating. Or maybe you are delighted that you’ll be taking more math! Students have completely different experiences of mathematics courses, and here we would like to lay out some reasons that all students should be excited about taking math.  

You have probably heard the refrain “Math is everywhere!” many times before, and it’s true: math IS everywhere. From computing your GPA (a weighted average) to understanding how debt works (compounding interest), math runs through most facets of our lives, and increasingly in the data driven industry. For instance, how should a large trucking company allocate its storage of empty trailor around the country to minimize the number of  miles empty trailors travel? This is a difficult math problem that generates jobs and saves the environment!

In practical terms, even if you do not choose to do a math major, a number of other majors - and professions! - require math. The most common ones are:

• MTH 111 Calculus I (Economics, Engineering, Physics, Statistics & Data Science, Pre-health)

• MTH 112 Calculus II (Engineering, Physics)

• MTH 153 Discrete Math (Computer Science)

• MTH 211 Linear Algebra (Statistics & Data Science)

• MTH 212 Calc III (Engineering, Physics)

• SDS/MTH 220  Intro to Probability and Stats (Statistics & Data Science, Biology, Economics; recommended for Engineering and Pre-health)

What courses am I prepared to take?   

A student who wishes to study mathematics may place herself according to the following guidelines.

• Any student who is curious about mathematics outside of the standard fields seen in high school may consider Discovering Mathematics (MTH105). Some incarnation of the course have explored arts and math, the role of chance in our lives, and measuring social inequalities.

• A student with three years of high school math (typically one year of geometry and two years of algebra) is ready for Elementary Functions (MTH102), which can prepare them to take Calculus I.

• A student with four years of high school math (but little or no calculus) can take Calculus I (MTH111).

• A student with a year of high school calculus is ready to take Discrete Mathematics (MTH153) or Calculus II (MTH112).

• Well-prepared students might start at Smith with Linear Algebra (MTH211)  or Calculus III (MTH212).

Below is a more detailed document matching your preparation with possible courses.

Mathematics, Statistics, and You 

Mathematics, Statistics, and You 

For statistics courses you are prepared to take, consult this Statistics and Data Science page.

For detailed information about the introductory calculus courses as Smith, including how they work and they help you do the things you want to do with your time at Smith, visit the Introductory Mathematics Courses at Smith website. 

The introductory calculus courses (MTH111: Calculus 1 and MTH112: Calculus 2) at Smith are offered in small sections of 20-28 students, taught by different professors. The sections of each introductory course are closely coordinated to maximize the resources available to students and make it easy for students to work together during the semester. Those resources include department peer tutors, quantitative skills tutors through the Spinelli Center for Quantitative Learning, and the department Calculus Training Group program, profiled in Grecourt Gate in November 2017. 

For those who either do not intend to take Calculus or who have already taken enough of it, there is math besides Calculus!

MTH153: Introduction to Discrete Mathematics

Description: An introduction to discrete (finite) mathematics with emphasis on the study of algorithms and on applications to mathematical modeling and computer science. Topics include sets, logic, graph theory, induction, recursion, counting and combinatorics.

Offered: Every semester

Prerequisite:  None, but MTH111 and familiarity with summation notation is recommended

Great for: Computer Science, Mathematics & Statistics, Statistics & Data Science – the study of logic and algorithms is necessary for good coding. In addition, you learn a variety of proof techniques, which are key for going deeper in mathematics as a whole.

MTH211: Linear Algebra

Description: Systems of linear equations, matrices, linear transformations, vector spaces. Applications to be selected from differential equations, foundations of physics, geometry and other topics.

Prerequisite: MTH 112 or the equivalent, or MTH 111 and MTH 153; MTH 153 is suggested

Offered: Every semester

Great for: Almost everyone, but specifically Computer Science, Mathematics & Statistics, Statistics & Data Science, Economics. Linear algebra is the workhorse subject of modern mathematics. Any work with data relies on an understanding of matrices. Linear algebra is even used to help identify exoplanets in astronomy! It turns up pretty much everywhere.  

Required for: MTH and SDS majors.

MTH212: Calculus III

Description: Theory and applications of limits, derivatives and integrals of functions of one, two and three variables. Curves in two and three dimensional space, vector functions, double and triple integrals, polar, cylindrical, spherical coordinates. Path integration and Green’s Theorem.

Prerequisites: MTH 112. It is suggested that MTH 211 be taken before or concurrently with MTH 212.

Offered: Every semester

Great for: Physics, Engineering, Mathematics & Statistics, Economics. Calculus III takes everything from calculus and moves into multiple dimensions. For physics and engineering, understanding of more than one dimension is essential for modeling how objects move through our multi-dimensional space. In economics, you often need to optimize quantities with many different inputs (and sometimes outputs!) which Calculus III can do.

Required for: EGR and MTH majors.

MTH/SDS220: Introduction to Probability and Statistics

Description: An application-oriented introduction to modern statistical inference: study design, descriptive statistics; random variables; probability and sampling distributions; point and interval estimates; hypothesis tests, resampling procedures and multiple regression. A wide variety of applications from the natural and social sciences are used. Classes meet for lecture/discussion and for a required laboratory that emphasizes analysis of real data.

Prerequisite: MTH 111 or the equivalent, or permission of the instructor. Lab sections limited to 20

Offered: Every semester

Great for: Everybody. Data analysis is a growing field and understanding how to work with data is useful in many fields. MTH 220 satisfies the basis requirement for biological science, engineering, environmental science, neuroscience and psychology.

Required for: BIO, EGR, ESP, NSC, PSY, SDS.  

Note: Other departments offer statistics courses with different prerequisites, and for which SDS 220 may be substituted (e.g. PSY/SDS 201, ECO 220)

Consult the Smith College Course Catalog for information on the current courses available in mathematics and statistics.

There are also several courses that are available for credit from other departments, including art, psychology and more. Consult the catalog.

What classes you should take depends a great deal on what you find most interesting and on what your goals are. Discuss your options with your adviser and also talk to the instructors of particular courses that interest you.

If you are interested in the sciences

The department offers a variety of courses to give you a solid mathematical experience. Calculus III and Linear Algebra are fundamental courses. You may also want to consider taking one or more of the following: Intro to Probability and Statistics, Differential Equations, Differential Equations and Numerical Methods, Discrete Mathematics, Advanced Topics in Continuous Applied Mathematics.

If you are interested in computer science

Consider taking some of these: Calculus III, Linear Algebra, Modern Algebra, Discrete Mathematics. Many of our students are double–majoring in mathematics and computer science.

If you are interested in economics

Calculus will give you a good, basic experience. You may consider other courses as well, so be sure to discuss your options with your adviser. If you are contemplating graduate school in economics, the economics department recommends you to take MTH 211, 212, 280 and 281. Taking a solid course in statistics is also a good idea (any of MTH 220, 246, 290, 291 and 320 would do). Many economics majors want to take MTH 264 as well. Double–majoring in mathematics and economics is a good choice.

If you are interested in applied mathematics

The following courses work specifically with applications: MTH 205, 264, 353 and 364. Other courses that contain many applications and are important for anyone considering graduate school in applied mathematics are: MTH 220, 246, 254, 255, 280, 290, 291, and 320. 

If you are interested in theoretical mathematics

The following courses work with abstract structures: MTH 233, 238, 246, 254, 255, 280, 281, 333, 370, 381, and 382.

If you liked calculus

There are many reasons for liking calculus. If you delighted in the geometry, for example, you should consider MTH 270, 280, 370 and 382. If you enjoyed the power of calculus to describe and understand the world, you will want to take MTH 264. If you are fascinated with the ideas of limit and infinity and want to get to the bottom of them, you should take MTH 281.

If you liked linear algebra

You will like MTH 233 very much, and you will also like MTH 238 and 333.

If you liked discrete mathematics

The natural sequel to Discrete Mathematics is MTH 254 or 255 and then 353. In addition, you may be interested in MTH 246 and in CSC 252 (counts 2 credits toward the mathematics major).

If you are interested in graduate school in mathematics

Take a lot of courses, but be sure to take MTH 233, 254, and 281 and as many of MTH 264, 333, 370, 381, and 382 as possible. You should also consider taking a graduate course at the University of Massachusetts.

If you are interested in graduate school in statistics

The MST Mathematical Statistics joint Major between MTH and SDS is explicitly designed as a preparation for graduate school in Statistics. 

If you are interested in graduate school in operations research

Operations research is a relatively new subarea of mathematics, bringing together mathematical ideas and techniques that are applied to large organizations such as businesses, computers, and governments. You should take MTH 211 and at least some of the courses listed for statistics above, some combinatorics (MTH 254) and some computer science. Consider also Topics in Applied Mathematics and Numerical Analysis.

If you want to be a teacher

Certification requirements vary widely from state–to–state. If you are interested in teaching in secondary school, a mathematics major plus practice teaching may be enough to get started. In Massachusetts, the major should include either MTH 233 or 238 and one of MTH 220 or 246. A course involving geometry, such as MTH 270 or MTH 370 is also helpful. You should also have some introduction to computers. For guidelines, look at the list of courses listed in the MAT program. Finally, while MTH 307 Topics in Mathematics Education is rarely offered, something equivalent is taught as a special studies whenever there are MAT students.

If you are interested in teaching elementary school, most of your required courses will be in the education department. In the mathematics department, our concern would be that you are comfortable with mathematics, have seen its variety, and most important, that you enjoy it. For all that, you should take the mathematics courses which appeal to you most. For education courses, the latest information is that you should take EDC 235, 238, 346, 347, 404 (practice teaching), and one elective to be certified. Note that during the semester when you take practice teaching EDC 404, you will likely be unable to take a math course. Plan ahead and consult the education department.

If you want to be a doctor

You are doing fine by majoring in mathematics. A course in statistics would be a very good idea. Other areas of mathematics that would be useful are differential equations and combinatorics.

If you want to be an actuary

Take MTH 246, 290, 291 and 320 and the actuarial exams that are offered periodically. Advancement as an actuary is achieved by passing of a series of examinations. Informal student study groups often form (ask around!).

If you want to get a good job when you graduate

A major in mathematics prepares you well, regardless of which courses you choose. Math majors learn to think on their feet; they aren't frightened of numbers and they're at home with abstract ideas. Often, this alone is what employers are looking for. That said, we should add that knowledge of computer programming is very useful, as is some familiarity with statistics.

If you want something Smith does not offer

If you are interested in a subject we do not offer, you should talk to professors whose fields of interest are closest to the subject, as a special studies. The arrangement must be approved by the department, but reasonable requests are not refused. If your interest is particularly strong, you might consider an honors project, or summer research work. You should also consider taking a course (or courses) at one of the consortium schools.

Postbaccalaureate Program

Sponsored by the Center for Women in Mathematics, the Postbaccalaureate Program is for women with bachelor's degrees who did not major in mathematics or whose mathematics major was light. This program is open to all women who have graduated college with some course work in mathematics above the level of calculus, and a serious interest in further pursuing mathematics. More information about the program is provided by the Center for Women in Mathematics.

Masters of Arts in Teaching

The Department of Mathematics and Statistics cooperates with the Department of Education and Child Study to offer a one–year Master of Arts in Teaching (MAT) program.

During one summer and two semesters, MAT candidates take three courses in mathematics and all the course work required for secondary teacher certification in Massachusetts. The program includes a semester–long internship in a local school. Applicants for the MAT program in mathematics should have an undergraduate degree in mathematics. College graduates with a different major will be considered if their undergraduate education included a strong foundation in mathematics.

Fifth-Year Master of Science in Statistics

Qualified graduates of the Department of Mathematics and Statistics can apply to the University of Massachusetts Amherst to earn a master's degree in statistics in a fifth year. Learn more about the program.