Mathematics Major and Minor

• Majors Offered by the Department

  The Department of Mathematics and Statistics offers a major that gives students a choice among three focuses that each address the above learning goals in a distinctive way:

  1. Major: Mathematics (focus in pure math)
  2. Major: Mathematics (focus in statistics)
  3. Major: Mathematics (focus in applied math)

  Major Requirements

  • Calculus II (MATH H118)
  • Multivariable Calculus (MATH H121 or MATH H216)
  • Linear Algebra (MATH H215)
  • Junior Seminar (MATH H299)
  • Senior Seminar (MATH H399)
  • Senior Research (MATH H400), including a senior paper and oral presentation
  • Five courses in the student’s chosen focus (see below)

  Focus Requirements in Pure Math

  • Two of the following courses: Analysis (MATH H317), Algebra (MATH H333), Topology (MATH H335)
  • Three additional math courses 200-level or higher (excluding Junior or Senior Seminar, Senior Research, Teaching Assistant, Independent Study), of which:
    • at least one must be in pure math, and
    • at least one must be outside of pure math, and
    • at least one must be 300-level, and
    • at most one can be cross-listed with another department.

  Focus Requirements in Statistics

  • A course in introductory statistics (STAT H203, ECON H203, ECON H204, PSYC H200, or SOCL H215)
  • Applied Multivariate Statistical Analysis (STAT H361)
  • Probability (MATH H218)
  • Two additional courses from the following list: Mathematical Statistics (STAT H328), Advanced Topics in Statistics (STAT H396), Analysis (MATH H317)

  Focus Requirements in Applied Math

  • Differential Equations (MATH H204)
  • Analysis (MATH H317)
  • Two courses, of which at least one is 300-level, from the list below:
    • Linear Optimization (MATH H210)
    • Scientific Computing: Continuous Systems (MATH H222)
    • Modeling and Differential Equations (MATH H382)
    • Partial Differential Equations (MATH H383)
    • Constrained and Combinatorial Optimization (MATH H384)
    • Advanced Topics in Applied Math ( MATH H397 and/or MATH B325); can be taken more than once if topics are sufficiently different)
  • One additional applied math course, which must be 300-level if a 200-level course was used as part of fulfilling the previous requirement. This additional course could be, but does not have to be, a third course from the list above. We have posted on our webpage a list of courses that are pre-approved as counting towards this requirement.

  Senior Project

  A senior paper is written by each major in close coordination with a faculty member. The senior paper is a year-long research project that includes both a written thesis and an oral presentation.  All seniors take a year-long senior seminar to support the senior paper. In the seminar, students learn how to use library resources, produce a mathematical document, and take turns presenting portions of their senior papers to each other to develop their skills in constructing and giving oral presentations.

   

  In the fall of the senior year, the student begins to focus on a topic (sometimes an interesting theorem, other times building a mathematical model or analyzing a data set) and works through the material with the faculty advisor. The student completes a detailed thesis proposal, an annotated bibliography, a "mini-paper," and a core fragment of the thesis. In the spring, the student develops the first draft, the second draft, and the final draft of the thesis, and concludes by presenting the thesis to faculty and fellow students.

  Senior Project Learning Goals

  Our students will engage with advanced content and techniques in pure mathematics, applied mathematics or statistics. They will gain ownership of the process and material through understanding the content and the details of the problem they are investigating, constructing illustrative examples, carrying out novel computations or carefully analyzing a data set. Our students will write clear, careful and correct mathematics/statistics, from precise definition or description of a model to rigorous proofs or well-supported analyses. They will develop an oral presentation that highlights the central ideas of their thesis work at a level appropriate for an audience in the mathematical/statistical sciences.

  Senior Project Assessment

  The grade for the senior thesis is determined by the following:

  • Level of engagement with advanced mathematics or statistics.
  • Level of ownership of the material and of the writing process.
  • Adherence to professional standards of written mathematics and statistics.

  The grade for the senior seminar is determined by the following:

  • Completing all the assignments in accordance with the assignment description.
  • Meeting deadlines for each assignment.
  • Quality of intermediate drafts, including whether easily discernible progress has been made from one assignment to another.
  • Engaged participation in seminar meetings.
  • Quality of the thesis presentation.

  Policies Related to Major Requirements

  • In reviewing student thesis topic proposals, the department will prioritize proposals where the topic is in the student's focus, to the extent possible given thesis advisor availability in that focus. 
  • If a student places past a course listed as required, that requirement is waived, but the student must take an additional course that counts for the major at the 200-level or higher (excluding Junior or Senior Seminar, Senior Research, Teaching Assistant, Independent Study).  For example, a student placed past MATH 118 would need to take 1 additional course; a student placed past MATH 121 would need to take 2 additional courses; a student placed past STAT 203 who chooses statistics as their focus would need to take an additional course along with any additional courses implied by their calculus placement.
  • In order to develop a connection between a student and the pool of potential thesis advisors, a major must take at least one course in their chosen focus at Haverford; exceptions to this rule are granted if, at the time of major declaration, the student gets approval from the department chair of a course plan that develops that connection in a different way.
  • A student’s transcript can only show one focus, but can minor in a second focus area in certain combinations (see below).
  • In the atypical circumstance that a student elects to graduate in seven semesters, they must inform the department of this choice when they declare their major in the spring of their sophomore year and complete the senior seminar and senior paper during the fall and spring of their junior year, i.e., during their fifth and sixth semesters.  (This means that students have to complete Math 299 (Junior Seminar) before the 5th semester.)
  • Students who graduate nine or more semesters after matriculating should make every effort to complete the Senior Seminar and senior paper during a single academic year (fall then spring), but students in this circumstance can complete these requirements “off-cycle” (spring then fall) with permission of the department chair.  This permission should be sought as soon as the student knows of their interest in an off-cycle thesis, and no later than the spring pre-registration immediately preceding their proposed spring-fall thesis year.  Off-cycle thesis students may have limited options for thesis advisors, since their spring-fall thesis year will overlap with two different fall-spring faculty sabbatical periods.
  • If a student elects to spend the whole junior year abroad, they must complete Math 299 (Junior Seminar) before the 5^th semester and inform the department of this choice when they declare their major in the spring of their sophomore year.

• Minors Offered by the Department

  • Minor: Pure Math
  • Minor: Statistics
  • Minor: Applied Math

  Pure Math Minor Requirements

  • Calculus II (MATH H118)
  • Multivariable Calculus (MATH H121 or MATH H216)
  • Linear Algebra (MATH H215)
  • Two of the following courses: Analysis (MATH H317), Algebra (MATH H333), Topology (MATH H335)
  • One additional course in pure math (a third course from the previous requirement, or another 200- or 300-level course in pure math)

  Statistics Minor Requirements

  • Multivariable Calculus (MATH H121 or MATH H216)
  • Linear Algebra (MATH H215)
  • A course in introductory statistics (STAT H203, ECON H204, PSYC H200, or SOCL H215)
  • Probability (MATH H218)
  • Advanced Multivariate Statistical Analysis (STAT H361)
  • One additional course in statistics from the following list: Mathematical Statistics (STAT H328), Advanced Topics in Statistics (STAT H396), or Advanced Econometrics (ECON H324)

  Applied Math Minor Requirements

  • Calculus II (MATH H118)
  • Multivariable Calculus (MATH H121 or MATH H216)
  • Linear Algebra (MATH H215)
  • Differential Equations (MATH H204)
  • Two additional courses in applied math, of which at least one must be at the 300-level; these two courses should come from the following list (or be approved as a substitution):
    • Modeling and Differential Equations (MATH H383)
    • Partial Differential Equations (MATH H383)
    • Scientific Computing: Continuous Systems (MATH H222)
    • Linear Optimization (MATH H210)
    • Constrained and Combinatorial Optimization (MATH H384)
    • Advanced Topics in Applied Math (MATH H397 and/or MATH B325); can be taken more than once if topics are sufficiently different)

  Policies Related to Minor Requirements

  • If a student places past a course listed as required, that requirement is waived, but the student must take an additional course that counts for the minor at the 200-level or higher (excluding Junior or Senior Seminar, Senior Research, Teaching Assistant, Independent Study).  For example, a student placed past MATH 118 would need to take 1 additional course; a student placed past MATH 121 would need to take 2 additional courses; a statistics minor placed past STAT 203 would need to take an additional course along with any additional courses implied by their calculus placement.
  • A pure math minor cannot be combined with a math major (focus in pure math) or with a math major (focus in applied math).
  • An applied math minor cannot be combined with a math major (focus in pure math) or with a math major (focus in applied math).
  • A statistics minor cannot be combined with a math major (focus in statistics).
  • Other than the case discussed in the previous bullet point, a minor in our department can be combined with a major, minor, or concentration (inside or outside of our department) as long as three or fewer courses are “double-counted”.  For example:
    • A student could complete a “Minor in statistics” and a “Concentration in Mathematical Economics” (as an economics major) if they use MATH 215, 216, and 218 to fulfill minor and concentration requirements, and then have no overlap in the courses they use to satisfy the remaining requirements.
    • A student who places past MATH 118 would replace the MATH 118 major requirement by an additional 200-level course of their choosing (as per a major requirement policy above).  Such a student could complete a "Major in Math (with focus in applied math)" and a "Minor in statistics" if they use MATH 121 and 215 to satisfy requirements for both the major and the minor, and MATH 218 to satisfy a minor requirement and as their “additional course” (replacing 118) for the major, and then have no overlap in the courses they use to satisfy the remaining requirements.

  For further information about the statistics minor, please see the PDF supplement on the mathematics website, or contact the minor coordinator.

Associated Programs and Concentrations

• Computer Science Major, Minor, and Concentration
• Mathematical Economics Concentration
• Scientific Computing Concentration