Mathematics and Statistics

Chair: Douglas Hundley

Adriana Ortiz Aquino

Barry Balof

Will Boyles

Russell A. Gordon

Patrick W. Keef

Matthew N. Petersen

Marina Ptukhina

Albert W. Schueller

 

About the Department

Mathematics and Statistics courses provide an opportunity to study mathematics and statistics for its own sake and as a tool for use in the physical, social, and life sciences.

All or part of the calculus sequence is required or recommended by several majors at Whitman and calculus is the most common mathematics course taken by students. However, the department offers other courses (Mathematics 128) that are intended for students who wish to take mathematics but are not familiar with calculus.

Learning Goals

Upon completing their degree, a student majoring in Mathematics will:

  • Be familiar with examples of the application of mathematics and/or statistics to other fields.
  • Be prepared for advanced undergraduate study in mathematics and statistics. In particular:
    • Be able to write correct and coherent mathematical arguments.
    • Understand foundational mathematical ideas related to formal logic, number theory, sets, functions and relations.
  • Understand core ideas of advanced undergraduate mathematics, including:
    • Fundamental concepts from real analysis (e.g., continuity, differentiation, and integration).
    • Mathematics majors: Fundamental concepts from abstract algebra (e.g., groups, rings, and fields).
    • Mathematics/Statistics majors: Fundamental concepts from probability theory and statistics (e.g., probability distributions, statistical inference, statistical modeling, ability to visualize data and create comprehensive data analysis reports).
  • Be able to independently investigate an advanced topic in mathematics or statistics and to report the results of that investigation in a clear and organized manner, both orally and in writing.

Distribution

For students who started at Whitman College prior to Fall 2024, the following courses count toward the quantitative analysis distribution rea: Mathematics 124, 125, 126, 128, 225, and 247.

For students who start at Whitman College in Fall 2024 or later, please refer to the General Studies section for a full list of courses that count toward each distribution area.

Advisory Information

Choosing a Calculus Course: Students who wish to take calculus should note the following: Students with a strong background in high school mathematics not including calculus start with Mathematics 124 or 125. Students who have taken a high school course in calculus, but who have not taken the BC calculus Advanced Placement Test (see the statement below regarding college credit for the Advanced Placement Test) should take the Advisory Calculus Placement exam offered by the Department of Mathematics and Statistics.

Advanced Placement: The policy for advanced standing and credit for the College Board Advanced Placement program is as follows:

  • Students with a 4 or 5 on the BC Calculus test are considered to have completed the equivalent of Mathematics 124 or 125 and 126 and receive six credits in Mathematics.
  • Students with a 4 or 5 on the AB Calculus test (or on the AB subtest of the BC test) are considered to have completed the equivalent of Mathematics 124 or 125 and receive three credits in Mathematics. These students should take the placement test offered by the department of Mathematics and Statistics to determine whether they should enroll in Mathematics 126 or Mathematics 225. Students receive transfer credit for Mathematics 124 or 125 only, even if they start in Mathematics 225.
  • Students with a 4 or 5 on the Statistics test are considered to have completed the equivalent of Mathematics 128 and receive three credits in Mathematics. Students should consider taking Mathematics 247 if they have also completed the equivalent of Mathematics 124 or 125.

A student has the option of repeating a course for which AP credit has been granted, but with a commensurate reduction in Advanced Placement credit.

GCE (Cambridge International) A-Level Exam students with an A*, A or B on the A-Level Mathematics Exam are considered to have completed the equivalent of Mathematics 124 or 125 and receive three credits in Mathematics.

P-D-F Policy: The department places no restrictions on the use of the P-D-F option for Mathematics courses for majors or non-majors, except that students choosing the Mathematics major must take Mathematics 225, 240, and 260 for grades. The department strongly recommends that students majoring in Mathematics or completing a joint major with Mathematics not use the P-D-F option in Mathematics and Statistics courses.

Programs of Study

Courses

Credits 4

Topics include limits and continuity. Definition, computation and applications of the derivative. An introduction to integration, including the fundamental theorem of calculus. Of the 4 credits, approximately 1 credit will be committed to a parallel track of instruction that introduces and/or reviews topics in algebra, trigonometry, exponential and log functions and graphing as they are being encountered in the calculus curriculum.

Distribution Area
Students entering Fall 2024 or later: Quantitative Analysis (QA)
Students entering prior to Fall 2024: Quantitative Analysis (QU DIST)
Prerequisites

Two years of high school algebra; and one year of plane geometry.

Credits 3

Topics include limits and continuity. Definition, computation and applications of the derivative. An introduction to integration, including the fundamental theorem of calculus.

Distribution Area
Students entering Fall 2024 or later: Quantitative Analysis (QA)
Students entering prior to Fall 2024: Quantitative Analysis (QU DIST)
Prerequisites

Two years of high school algebra, one year of plane geometry, and knowledge of trigonometry and exponential/logarithmic functions; or consent of instructor.

Credits 3

A continuation of Mathematics 125, covering techniques for computing indefinite integrals, applications of the definite integral, infinite sequences and series, Taylor polynomials and power series.

Distribution Area
Students entering Fall 2024 or later: Quantitative Analysis (QA)
Students entering prior to Fall 2024: Quantitative Analysis (QU DIST)
Prerequisites

Mathematics 124 or 125; or equivalent.

Credits 3

This course introduces students to basic tools for describing and summarizing data as well as methods of statistical inference such as confidence intervals and hypothesis tests.  The randomization approach used in the course allows students to develop a deeper understanding of the fundamental idea of statistical inference. A web-based statistical applet is used throughout the course. This course does not count toward the Mathematics major or Data Science minor. Students considering these should enroll in Mathematics 247 instead.

Distribution Area
Students entering Fall 2024 or later: Quantitative Analysis (QA)
Students entering prior to Fall 2024: Quantitative Analysis (QU DIST)
Prerequisites

two years of high school mathematics.

Credits 1 Max Credits 3

On occasion, the mathematics and statistics department will offer courses on introductory topics in mathematics and statistics that are not generally covered in other introductory courses. Possible topics include Introduction to Number Theory, Chaos and Applied Discrete Probability. See course schedule for any current offerings.

Credits 4
Cross-Listed

An introduction to the approaches and tools of exploratory data analysis and visualization. Through a series of projects, we explore large data sets through methods like cleaning, filtering, sorting, boolean selections and merging. As large amounts of data typically are stored in lists, we use algorithmic thinking to transform raw data into usable form. We develop hypotheses and supporting visualizations to tell the story of the data. We learn and practice technical communication in both oral and written form. Through a series of readings and discussions, we learn best practices for the ethical use of data and how to identify problematic uses of data in society. May be elected as Computer Science 215.

Distribution Area
Students entering prior to Fall 2024: Quantitative Analysis (QU DIST)
Prerequisites

Mathematics 124 or 125; and Computer Science 167 or 270.

Credits 3
Cross-Listed

This course provides a mathematical foundation for formal study of algorithms and the theory of computing. It also introduces functional programming, a powerful computing paradigm that is distinct from the imperative and object-oriented paradigms introduced in Computer Science 167. Students will practice formal reasoning over discrete structures through two parallel modes: mathematical proofs and computer programs. We will introduce sets and lists, Boolean logic, and proof techniques. We will explore recursive algorithms and data types along with mathematical and structural induction. We consider relations and functions as mathematical objects and develop idioms of higher-order programming. We consider applications useful in computer science, particularly counting sets. May be elected as Computer Science 220.

Distribution Area
Students entering Fall 2024 or later: Quantitative Analysis (QA)
Prerequisites

Computer Science 167 or 270; and Mathematics 124 or 125.

Credits 4

Topics include three dimensional geometry, partial derivatives, gradients, extreme value theory for functions of more than one variable, multiple integration, line integrals, and various topics in vector analysis.

Distribution Area
Students entering Fall 2024 or later: Quantitative Analysis (QA)
Students entering prior to Fall 2024: Quantitative Analysis (QU DIST)
Prerequisite Courses
Credits 3

This course first considers the solution set of a system of linear equations. The ideas generated from systems of equations are then generalized and studied in a more abstract setting, which considers topics such as matrices, determinants, vector spaces, inner products, linear transformations, and eigenvalues.  

Prerequisite Courses
Credits 3

This course includes first and second order linear differential equations and applications. Other topics may include systems of differential equations and series solutions of differential equations.

Prerequisite Courses
Credits 3

An introduction to statistics for students who have taken at least one course in calculus. This course focuses on introducing statistical concepts and inference through active learning assignments. Students learn about the process of statistical investigations. This includes data collection and exploration, methods of statistical inference,  and the ability to draw appropriate conclusions.  The widely-used statistical software R will be used in addition to web-based applets.

Distribution Area
Students entering Fall 2024 or later: Quantitative Analysis (QA)
Students entering prior to Fall 2024: Quantitative Analysis (QU DIST)
Prerequisites

Mathematics 124 or 125; or equivalent.

Credits 3

This course follows introductory statistics by investigating more complex statistical models and their application to real data. The topics may include simple linear regression, multiple regression, non-parametric methods, and logistic regression. A statistical software package will be used. Familiarity with R is expected.

Prerequisites

Mathematics 247 or Economics 227; or consent of instructor.

Credits 4

An introduction to some of the concepts and methodology of advanced mathematics, including a brief introduction to number theory. Emphasis is on the notions of rigor and proof. This course is intended for students interested in majoring in mathematics and statistics; students should plan to complete it no later than the spring semester of the sophomore year.

Prerequisite Courses
Credits 1 Max Credits 3
Faculty
Staff

A reading project in an area of mathematics and statistics not covered in regular courses or that is a proper subset of an existing course. The topic, selected by the student in consultation with the staff, is deemed to be introductory in nature with a level of difficulty comparable to other mathematics and statistics courses at the 200-level. May be repeated for a maximum of six credits.

Prerequisites

Consent of instructor.

Credits 3

This independent study in geometry will include a review of high school geometry, a few topics in advanced Euclidean geometry, a reading of Books I and II of Euclid's Elements, and an introduction to hyperbolic geometry. The grading for the course will be based on a journal (40%), a two-hour written midterm exam (30%), and a one-hour oral final exam (30%). Since the student will be working independently on the material, a disciplined work ethic is required.

Prerequisites

Mathematics 225 and consent of instructor.

Credits 1

Students will meet weekly to discuss problem-solving techniques. Each week a different type of problem will be discussed. Topics covered will include polynomials, combinatorics, geometry, probability, proofs involving induction, parity arguments, and divisibility arguments. The main focus of the course will be to prepare students for the William Lowell Putnam Mathematics Competition, a national examination held the first Saturday in December. Students who place in the top 500 on this exam nationwide have their names listed for consideration to mathematics graduate programs. Graded credit/no credit. May be repeated for a maximum of four credits.

Prerequisites

Mathematics 260 or consent of instructor.

Credits 3
Cross-Listed

Which problems can be solved computationally? Which cannot? Why? We can prove that computers can perform certain computations and not others. This course will investigate which ones, and why. Topics will include formal models of computation such as finite state automata, push-down automata, and Turing machines, as well as formal languages such as context-free grammars and regular expressions. May be elected as Computer Science 320, and must be elected as Computer Science 320 to apply toward the total credit requirement in Computer Science.   

Prerequisites

Computer Science/Mathematics 220; or Mathematics 260.

Credits 3
Cross-Listed

How can we be confident that an algorithm is correct before we implement it?  How can we compare the efficiency of different algorithms? We present rigorous techniques for design and analysis of efficient algorithms. We consider problems such as sorting, searching, graph algorithms, and string processing. Students will learn design techniques such as linear programming, dynamic programming, and the greedy method, as well as asymptotic, worst-case, average-case and amortized runtime analyses. Data structures will be further developed and analyzed. We consider the limits of what can be efficiently computed. May be elected as Computer Science 327, and must be elected as Computer Science 320 to apply toward the total credit requirement in Computer Science.  

Prerequisites

Computer Science 270; and Computer Science/Mathematics 220 or Mathematics 260.

Credits 3

Essential for prospective high school mathematics teachers, this course includes a study of Euclidean geometry, a discussion of the flaws in Euclidean geometry as seen from the point of view of modern axiomatics, a consideration of the parallel postulate and attempts to prove it, and a discussion of the discovery of non-Euclidean geometry and its philosophical implications.

Prerequisite Courses
Credits 3
Cross-Listed

Operations research is a scientific approach to determining how best to operate a system, usually under conditions requiring the allocation of scarce resources. This course will consider deterministic models, including those in linear programming (optimization) and related subfields of operations research. May be elected as Computer Science 339.

Prerequisites

Mathematics 240; and Computer Science 167 or 270.

Credits 4

Statistical concepts and statistical methodology useful in descriptive, experimental, and analytical study of biological and other natural phenomena.  Course covers major design structures, including blocking, nesting and repeated measures (longitudinal data), and statistical analysis associated with these structures.

Prerequisites

Mathematics 247 or Economics 227.

Credits 3

A formal introduction to probability and randomness. The topics of the course include but are not limited to conditional probability, Bayes’ Theorem, random variables, the Central Limit Theorem, expectation and variance. Both discrete and continuous probability distribution functions and cumulative distribution functions are studied.

Prerequisite Courses
Credits 3
Cross-Listed

This course explores the process of machine learning through the lens of empirical modeling. We will develop the theory and algorithms that underpin the process of learning interesting things about data. Algorithms we’ll develop typically include: singular value decomposition and eigenfaces, the n-armed bandit, projections and linear regression, data clustering (k-means, Neural Gas, Kohonen’s SOM), linear neural networks, optimization algorithms, autoencoders and deep networks. The course will involve some computer programming, so previous programming experience is helpful. May be elected as Computer Science 350. Prerequisite: Mathematics 240.

Prerequisite Courses
Credits 3

Topics in elementary combinatorics, including: permutations, combinations, generating functions, the inclusion-exclusion principle, and other counting techniques; graph theory; and recurrence relations.

Prerequisites

Mathematics 260; or consent of instructor.

Credits 3

An introduction to mathematics commonly used in engineering and physics applications. Topics may include: vector analysis and applications; matrices, eigenvalues, and eigenfunctions; boundary value problems and spectral representations; Fourier series and Fourier integrals; solution of partial differential equations of mathematical physics.

Prerequisite Courses
Credits 3

Complex analysis is the study of functions defined on the set of complex numbers. This introductory course covers limits and continuity, analytic functions, the Cauchy-Riemann equations, Taylor and Laurent series, contour integration and integration theorems, and residue theory.

Prerequisite Courses
Credits 1 Max Credits 3

See course schedule for any current offerings.

Credits 1 Max Credits 3

A reading project in an area of mathematics and statistics not covered in regular courses or that is a proper subset of an existing course. The topic, selected by the student in consultation with the staff, is deemed to be introductory in nature with a level of difficulty comparable to other mathematics and statistics courses at the 200-level. May be repeated for a maximum of six credits.

Prerequisites

Consent of instructor.

Credits 4

This course studies the mathematical theory of statistics with a focus on the theory of estimation and hypothesis tests. Topics may include properties of estimators, maximum likelihood estimation, convergence in probability, the central limit theorem, order statistics, moment generating functions, and likelihood ratio tests. A statistical software package will be used.

Prerequisites

Mathematics 349; and Mathematics 128, Mathematics 247, Economics 227, or Environmental Studies 207.

Credits 4

Provides a rigorous study of the basic concepts of real analysis, with emphasis on real-valued functions defined on intervals of real numbers. Topics include sequences, continuity, differentiation, integration, and infinite series. 

Prerequisite Courses
Credits 4

The content varies from instructor to instructor with typical topics chosen from series of functions, topology of the real line, basic concepts of metric spaces, the calculus of vector-valued functions, and more advanced integration theory.

Prerequisite Courses
Credits 3
Cross-Listed

An introduction to numerical approximation of algebraic and analytic processes. Topics include numerical methods of solution of equations, systems of equations and differential equations, and error analysis of approximations. May be elected as Computer Science 467.

Prerequisite or Corequisite

Mathematics 240.

Prerequisites

Computer Science 167 or 270.

Credits 1 Max Credits 3

On occasion, the mathematics and statistics department will offer courses on advanced topics in mathematics and statistics that are not found in other course offerings. Possible topics include topology, number theory, and problem-solving. See course schedule for any current offerings.

Credits 4

An introduction to groups, rings and fields, including subgroups and quotient groups, homomorphisms and isomorphisms, subrings and ideals.

Prerequisite Courses
Credits 4

Topics may include fields, simple groups, Sylow theorems, Galois theory, and modules.

Prerequisite Courses
Credits 1 Max Credits 3

A reading or research project in an area of mathematics and statistics not covered in regular courses. The topic is to be selected by the student in consultation with the staff. Maximum of six credits.

Prerequisites

Consent of instructor.

Credits 4

Preparation of the senior project required of all graduating mathematics majors. Each student will be matched with a faculty member from the mathematics and statistics department who will help supervise the project. Course objectives include developing students’ abilities to independently read, develop, organize, and communicate mathematical ideas, both orally and in writing. A final written and oral report on the project is completed.

Credits 4

Preparation of an honors thesis. Required of and limited to senior honors candidates in mathematics. Students will be a part of the Mathematics 497 Senior Project class (described above), but their work will be held to a higher standard.

Prerequisites

Admission to honors candidacy.