ÀÏÍõÂÛ̳

The Mathematics curriculum is designed to expose students to a wide spectrum of ideas in modern mathematics, train students in the art of logical reasoning and clear expression, and provide students with an appreciation of the beauty of the subject and of its vast applicability.

Students may complete a major or minor in Mathematics. Within the major, students may complete the requirements for secondary school certification. In addition, there are various programs that, for suitably advanced students, can be combined with the major. These include the combined A.B./M.A. program at ÀÏÍõÂÛ̳, and combined degree programs in engineering at the California Institute of Technology, Columbia University, and the University of Pennsylvania.

Major Requirements

The requirements in mathematics are designed to ensure that all students have a solid foundation in mathematical reasoning, both algebraic and analytic, as well as an appreciation for how mathematics can be used in applications. A common core of four key courses will lay the groundwork for additional exploration in the major. Students will achieve breadth in their program by exploring three main areas of mathematical thought: algebraic (AL), analytic (AN), and applied (AP). They will achieve depth in some areas of mathematical knowledge by taking a minimum of three courses at the 300-level.  Students will better understand how technology can (and cannot) be used to further mathematical understanding with an introduction to computational methods as part of the Transitions course (MATH B206), and they will develop their abilities to learn independently and communicate clearly, both orally and in written form, through completion of the Senior Conference (MATH B399).

All math majors must complete a minimum of 10 courses at the 200 level or above, including

• [Common Core] 
  • MATH B201: Multivariable Calculus (or MATH H121 or MATH H216)
  • MATH B203: Linear Algebra (or MATH H215)
  • MATH B206: Transitions to Higher Mathematics (WI). This course is a pre-requisite for all 300-level ÀÏÍõÂÛ̳ math courses.   
  • MATH B301: Real Analysis I (or MATH H317) or MATH B303: Abstract Algebra I (or MATH H334)
• [Breadth] Among the common core, depth, and elective choices, courses must include at least one course with each of the algebraic (AL), analytic (AN), and applied (AP) designations found in lists below.
• [Depth] A minimum of three 300-level (or 500-level) math courses including MATH B301 and/or MATH B303 but not including senior conference (MATH B398/399) or senior research (MATH B400/403).
• [Senior Capstone] One semester of Senior Conference MATH B398/399.

These requirements will apply to students who start at ÀÏÍõÂÛ̳ in fall 2022 or later (i.e. Class of '26). Students who started in fall 2021 have the option of following these requirements or the previous requirements (see below). Students starting in fall 2020 or earlier are governed by the previous requirements. Students who are unsure about which set of requirements to follow should consult the department.

Mathematics majors are encouraged to complete their core requirements other than Senior Conference by the end of their junior year. Senior Conference must be taken during the senior year.

Students considering the possibility of graduate study in mathematics or related fields are urged to go well beyond the minimum requirements of the major. In such cases, a suitable program of study should be designed with the advice of a major advisor.

The following is a list of courses that satisfy the Algebraic (AL) Requirement:

• MATH B221: Intro to Topology and Geometry;
• MATH B290: Elementary Number Theory;
• MATH B295: Combinatorics;
• MATH B303/H333: Abstract Algebra I;
• MATH B304/H334: Abstract Algebra II;
• MATH B312/B512/H335: Topology;
• MATH B317: Topics in Algebra;
• MATH B390: Number Theory;
• MATH H394: Advanced topics in Theoretical Computer Science and Discrete Math;
• MATH B503: Graduate Algebra I;
• MATH B504: Graduate Algebra II;
• MATH B525: Algebraic Topology;
• MATH H395: Advanced topics in Combinatorics.

 The following is a list of courses satisfying the Analysis (AN) Requirement:

• MATH B205/H218: Probability;
• MATH B210/H204: Differential Equations;
• MATH B261: Introduction to Harmonic Analysis and Wavelets;
• MATH B301/H317: Real Analysis I;
• MATH B302/H318: Real Analysis II;
• MATH B310: Mathematics of Financial Derivatives;
• MATH B311: Partial Differential Equations;
• MATH B312/B512/H335: Topology;
• MATH B322/B522: Complex Analysis;
• MATH/CMSC H340: Analysis of Algorithm;
• MATH/CMSC H345: Theory of Computation;
• MATH B390: Number Theory;
• MATH B501: Graduate Analysis I;
• MATH B502: Graduate Analysis II;
• MATH B530: Differential Topology;
• MATH H328 Mathematical Statistics;
• MATH H328: Mathematical Statistics;
• MATH H337: Differential Geometry.

The following is a list of courses satisfying the Applied (AP) Requirement:

• CHEM B221: Physical Chemistry I or CHEM H305 Quantum Chemistry;
• CHEM B321: Advanced Physical Chemistry;
• CMSC B231: Discrete Mathematics;
• CMSC B310: Computational Geometry;
• ECON B304/H304: Econometrics;
• PHYS B205: Math Methods 1;
• PHYS B207: Math Methods 2;
• PHYS B328: Galactic Dynamics and Mechanics;
• MATH H203: Statistical Methods and their Applications;
• MATH B205/H218: Probability;
• MATH B208: Modeling & Simulation;
• MATH B210/H204: Differential Equations;
• MATH H210: Linear Optimization;
• MATH H222: Scientific Computing: Continuous Systems;
• MATH B225: Financial Mathematics;
• MATH/STAT H286: Multivariate Statistical Analysis;
• MATH/STAT H286: Advanced Topics in Statistics;
• MATH/STAT H328: Mathematical Statistics;
• MATH B295: Actuarial Mathematics;
• MATH B295: Math Modeling & Sustainability;
• MATH B295: Combinatorics;
• MATH B295: Statistics with R;
• MATH/ B308: Applied Mathematics I;
• MATH B310: Math of Financial Derivatives;
• MATH/ B325: Advanced Topics in Applied Mathematics;
• MATH H360: Mathematical Economics;
• MATH H397: Advanced Topics in Applied Math: Mathematical Modeling.

When a course is listed in more than one breadth category, a student may choose in which category to count it. But a course may only be counted once for breadth. This list is not exhaustive. For the status of courses not on the list, students should consult the department.

For students declaring the math major in 2024-25 (or later), at most two courses can be doubled counted for a second major. For students who have declared the math major in 2023-24 or earlier, at most three courses can be doubled counted for a second major.

Major Writing Requirement

Students will take MATH B206: Transitions to Higher Mathematics, a writing intensive course, to satisfy the major writing requirement. Students will learn mathematical writing in the form of both proof and computer coding. This course will prepare students for the mathematical writing they will be doing at the 300 level.

Honors

The degree with honors will be awarded by the Department to students who complete the major in mathematics and satisfy the following two additional requirements.

1. Complete a thesis project.
   1. The thesis consists of a written project, which can be expository or contain original results, and an oral presentation of the thesis. The thesis typically involves two semesters worth of work.
   2. While doing their two semesters of thesis work, students will be enrolled in a research course (typically Math B400: Senior Research). These two semesters of research work do not count as electives towards fulfilling the major requirements. 
2. Display a high level of commitment to mathematics, which can be demonstrated in multiple ways, for example:
   1. Strong academic achievement demonstrated by a grade point average of at least 3.6 calculated using top grades from 10 math courses that complete the math major, or
   2. Successfully completing wtih a merit grade at least two additional mathematics courses beyond the requirements of the major and thesis, or    
   3. Engagement with mathematical activities outside of formal course work. This could include completing a summer research project or internship, strong dedication to TAing or tutoring in math, or leadership or persistent engagement in activities that contribute to supporting and strengthening our mathematical community (such as DMC, Problem Solving Seminar, SMARP Group, or serving as a Major Representative).

Students may, in consultation with their thesis advisor, petition the Department to adjust these requirements in unusual circumstances.

Minor Requirements

The math minor requires five courses in mathematics at ÀÏÍõÂÛ̳ or Haverford.

Two of the mathematics courses must be at the 300-level or higher and the remaining three courses must be at least at the 200-level or higher; the Haverford course, Math H121, Multivariable Calculus, can also be counted towards the math minor as if it were a 200-level course. Note that MATH B206: Transitions to Higher Mathematics is a pre-requisite for any 300-level math course at ÀÏÍõÂÛ̳. 

Any of the courses from other departments listed below in the Math Electives section can be counted as a mathematics course towards the minor. These courses may only be counted as 200-level courses for the purposes of the math minor, regardless of their course numbers within their own departments. At most one course may double-count towards both your major and the math minor.

It may also be possible to count certain math courses taken at other colleges and universities towards the math minor. This will always require special permission from the Mathematics Department.

Advanced Placement

Students entering with a 4 or 5 on the Calculus AB advanced placement test will be given credit for MATH 101 and could enroll in MATH 102 or MATH 201 as their first mathematics course. Students entering with a 4 or 5 on the Calculus BC advanced placement test will be given credit for MATH 101 and 102, and should enroll in MATH 201 as their first mathematics course. All other students are strongly encouraged to take the Mathematics Placement Exam so they can be best advised.

Previous Major Requirements 

These previous requirements apply to students who started at ÀÏÍõÂÛ̳ in fall 2020 or earlier. Students who started in fall 2021 have the option of following these previous requirements or the new requirments above. 

A minimum of 10 semester courses is required for the major, including the six core courses listed below and four electives at or above the 200 level. 

Core Requirements:

MATH B201 Multivariable Calculus (H121 or H216)
MATH B203 Linear Algebra (H215)
MATH B301 Real Analysis I (H317)
MATH B303 Abstract Algebra I (H333)
MATH B302 Real Analysis II (H318) or MATH B304 Abstract Algebra II (H334)
MATH B398 or B399 Senior Conference

The course numbers HXXX refer to Haverford College equivalents. With the exception of Senior Conference, equivalent courses at Haverford or elsewhere may be substituted for ÀÏÍõÂÛ̳ courses with approval of the major advisor.

MATH B301 and MATH B302 have been designated as Writing Attentive (WA). As the analysis and algebra sequences, MATH 301/302 and MATH 303/304, both have a strong proof writing focus, students often find it useful to take a course such as MATH 206 (Transition to Higher Mathematics) before they enroll in these sequences. 

The Department will change the core requirements in coming years. As a transition to this change, with permission of the Mathematics Department certain other 300-level or 500-level math courses may be substituted for MATH B302 or MATH B304. In particular for the 2023-2024 academic year, these include MATH B310 Math of Financial Derivatives, MATH B322 Functions of Complex Variables, MATH B325 Adv. Topics Applied Math, MATH B503 Graduate Algebra I, MATH B504 Graduate Algebra II, MATH B530 Differential Topology, and at Haverford, MATH H328 Mathematical Statistics, MATH H335 Topology, MATH H340 Analysis of Algorithms, MATH H345 Theory of Computation, MATH H360 Mathematical Economics, MATH H361 Applied Multivariate Statistical Analysis, MATH H382 Mathematical Modeling and Differential Equations, MATH H390 Advanced Topics in Algebra, and MATH H391 Advanced Topics in Geometry and Topology. 

Mathematics majors are encouraged to complete their core requirements other than Senior Conference by the end of their junior year. Senior Conference must be taken during the senior year.

Students considering the possibility of graduate study in mathematics or related fields are urged to go well beyond the minimum requirements of the major. In such cases, a suitable program of study should be designed with the advice of a major advisor.

Math Electives:

Any mathematics course at or above the 200-level (including graduate courses) or any course cross-listed as a mathematics course at ÀÏÍõÂÛ̳ or Haverford can be used as an elective towards the major.

In addition, some ÀÏÍõÂÛ̳ and Haverford courses from departments other than mathematics that have a substantial mathematical content may also be counted as electives. Currently, courses that count as math electives include:

• CHEM B221: Physical Chemistry I or CHEM H305 Quantum Chemistry;
• CHEM B321: Advanced Physical Chemistry;
• CMSC B231: Discrete Mathematics;
• CMSC B310: Computational Geometry;
• CMSC B340: Analysis of Algorithms;
• ECON B304/ECON H304: Econometrics;
• PHYS B205: Math Methods 1;
• PHYS B207: Math Methods 2;
• PHYS B328: Galactic Dynamics and Mechanics.

A student may also, in consultation with a major advisor, petition the Department to accept additional courses as electives.

At most three courses can be doubled counted for a second major.

Major Writing Requirement

Students will take two writing attentive courses to satisfy the major writing requirement. Courses that are designated as writing attentive are MATH B301 and MATH B303.

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