Exploring the University of Washington Mathematics Department: A Comprehensive Overview
The University of Washington (UW) boasts a distinguished Mathematics Department, dedicated to both teaching and cutting-edge research. This article delves into the department's offerings, research areas, curricular options, and commitment to fostering a vibrant mathematical community.
A Hub for Mathematical Exploration
The Department of Mathematics at UW offers a range of undergraduate and graduate degree programs. These programs emphasize mathematical theory while also exploring its connections to a wide array of applications. The department encourages analytical thinking, problem-solving skills, effective communication, and teamwork abilities.
The department's strength lies in its collaborative spirit. Students and faculty engage in projects with various UW departments, including Applied Mathematics, Statistics, Computer Science, Physics, and several engineering departments. This interdisciplinary approach allows for a broader understanding of how mathematics impacts different fields.
Diverse Research Landscape
Mathematics research at UW spans both classical and innovative areas. This includes interdisciplinary collaborations. The department's Washington Experimental Mathematics Lab (WXML) exemplifies this approach. It brings together students, faculty, and community members to work on experimental, computational, and visual projects.
The department's research falls into four broad categories:
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- Algebra & Combinatorics
- Analysis
- Geometry & Topology
- Applied Mathematics
Faculty members are passionate about their research and actively share their knowledge through collaborations and student mentoring.
Degree Programs and Curricular Options
The Department of Mathematics offers four degree programs, providing students with diverse paths to explore their mathematical interests:
- B.A. Standard: This option allows students to study a wide range of subjects, from algebra, analysis, and geometry to probability, combinatorics, and optimization.
- B.A. Philosophy: This option is tailored for students interested in the intersection of mathematics and philosophy.
- B.A. Teaching: This option is designed for students preparing to become secondary mathematics teachers.
- B.S. Mathematics: This program provides a more intensive and focused study of mathematics.
Mathematics is a minimum requirements major. Once a student meets the minimum requirements, they can be admitted without further screening. An application for general admission to the UW is required for all transfer students. Preparation for the major is a factor in transfer admission.
Course Offerings: A Glimpse
The department offers a wide array of courses, catering to different levels and interests. Here's a glimpse of some of the courses available:
MATH 098 Intermediate Algebra (0): Intermediate algebra equivalent to third semester of high school algebra. Includes linear equations and models, linear systems in two variables, quadratic equations, completing the square, graphing parabolas, inequalities, working with roots and radicals, distance formula, functions and graphs, exponential and logarithmic functions. Course awarded as transfer equivalency only.
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MATH 100 Algebra (5): Similar to the first three terms of high school algebra. Assumes no previous experience in algebra. Open only to students [1] in the Educational Opportunity Program or [2] admitted with an entrance deficiency in mathematics.
MATH 102 Algebra (5): Similar to the first three terms of high school algebra.
MATH 103 Introduction to Elementary Functions (5): Continues the study of algebra begun in MATH 100 and MATH 102 with emphasis on functions (polynomial, rational, logarithmic, exponential, and trigonometric).
MATH 108 International Baccalaureate (IB) Mathematical Studies (5): Course awarded based on International Baccalaureate (IB) score.
MATH 109 International Baccalaureate (IB) Standard Level Mathematics (5): Course awarded based on International Baccalaureate (IB) score.
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MATH 111 Algebra with Applications (5): Use of graphs and algebraic functions as found in business and economics. Algebraic and graphical manipulations to solve problems. Exponential and logarithm functions; various applications to growth of money. Recommended: completion of Department of Mathematics' Guided Self-Placement.
MATH 112 Application of Calculus to Business and Economics (5): Rates of change, tangent, derivative, accumulation, area, integrals in specific contexts, particularly economics. Techniques of differentiation and integration. Application to problem solving. Optimization. Credit does not apply toward a mathematics major. Course equivalent to: B MATH 144 and TMATH 122. Course overlaps with: MATH 124; Q SCI 291; STMATH 113; STMATH 114; STMATH 124; and TMATH 124. Prerequisite: a minimum grade of 2.0 in either MATH 111 or MATH 120, or a minimum score of 2 on the AP MATH AB exam.
MATH 115 Study Abroad Mathematics 1 (1-10, max. 15): Mathematics courses taken through a UW approved study abroad program.
MATH 116 Introduction to Taylor Polynomials and Taylor Series (1): Brief introduction to Taylor polynomials, error bounds, and Taylor series. Prerequisite: either a minimum grade of 2.0 in MATH 125, or a minimum score of 4 on BC advanced placement test.
MATH 120 Precalculus (5): Basic properties of functions, graphs; with emphasis on linear, quadratic, trigonometric, exponential functions and their inverses. Emphasis on multi-step problem solving. Maximum 10 credits allowed between TMATH 115; TMATH 116; TMATH 120; and MATH 120. Course equivalent to: TMATH 120. Course overlaps with: B MATH 123. Recommended: completion of Department of Mathematics' Guided Self-Placement.
MATH 124 Calculus with Analytic Geometry I (5): First quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus. Course equivalent to: STMATH 124 and TMATH 124. Course overlaps with: MATH 112; B MATH 144; STMATH 113; STMATH 114; and TMATH 122. Recommended: completion of Department of Mathematics' Guided Self-Placement.
MATH 125 Calculus with Analytic Geometry II (5): Second quarter in the calculus of functions of a single variable. Emphasizes integral calculus. Emphasizes applications and problem solving using the tools of calculus. Cannot be taken for credit if credit has already been earned for MATH 207. Course equivalent to: STMATH 125 and TMATH 125. Prerequisite: either minimum grade of 2.0 in MATH 124, score of 3 on AB advanced placement test, or score of 3 on BC advanced placement test.
MATH 126 Calculus with Analytic Geometry III (5): Third quarter in calculus sequence. Introduction to Taylor polynomials and Taylor series, vector geometry in three dimensions, introduction to multivariable differential calculus, double integrals in Cartesian and polar coordinates. Course equivalent to: STMATH 126 and TMATH 126. Course overlaps with: MATH 136. Prerequisite: either a minimum grade of 2.0 in MATH 125, a minimum grade of 2.0 in MATH 135, or a minimum score of 4 on BC advanced placement test.
MATH 134 Accelerated [Honors] Calculus (5): Covers the material of MATH 124, MATH 125, MATH 126; MATH 207, MATH 208. First year of a two-year accelerated sequence. May receive advanced placement (AP) credit for MATH 124 after taking MATH 134. For students with above average preparation, interest, and ability in mathematics.
MATH 135 Accelerated [Honors] Calculus (5): Covers the material of MATH 124, MATH 125, MATH 126; MATH 207, MATH 208. First year of a two-year accelerated sequence. May receive advanced placement (AP) credit for MATH 125 after taking MATH 135. For students with above average preparation, interest, and ability in mathematics. Prerequisite: a minimum grade of 2.0 in MATH 134.
MATH 136 Accelerated [Honors] Calculus (5): Covers the material of MATH 124, MATH 125, MATH 126; MATH 207, MATH 208. First year of a two-year accelerated sequence. For students with above average preparation, interest, and ability in mathematics. Course overlaps with: MATH 126. Prerequisite: a minimum grade of 2.0 in MATH 135.
MATH 180 Topics in Mathematics for Non-Science Majors (3/5, max. 10): Current topics in mathematics.
MATH 197 Problem Solving in Mathematics (2, max. 4): Lectures and problem sessions in mathematics with applications. Enrollment restricted to EOP students only. Credit/no-credit only.
MATH 198 Special Topics in Mathematics (1-5, max. 15): Independent reading in math. Does not count as credit toward a math major. Credit/no-credit only.
MATH 200 Discrete Mathematics I (5): Introduction to mathematical problem solving through explorations in discrete mathematics. Graph theory, enumerative combinatorics, probability, and elementary number theory.
MATH 201 Discrete Mathematics II (5): Further explores discrete mathematics. Covers set theory, probability, linear algebra, number theory and group theory.
MATH 207 Introduction to Differential Equations (4): Introductory course in ordinary differential equations. Includes first- and second-order equations and Laplace transform. Course overlaps with: STMATH 207 and TMATH 207. Prerequisite: a minimum grade of 2.0 in MATH 125.
MATH 208 Matrix Algebra with Applications (4): Systems of linear equations, vector spaces, matrices, subspaces, orthogonality, least squares, eigenvalues, eigenvectors, applications. For students in engineering, mathematics, and the sciences. Course overlaps with: BIS 231; STMATH 208; and TMATH 208. Recommended: completion of Department of Mathematics' Guided Self-Placement.
MATH 209 Linear Analysis (4): First order systems of linear differential equations, Fourier series and partial differential equations, and the phase plane. Prerequisite: either a minimum grade of 2.0 in both MATH 207 and MATH 208, or a minimum grade of 2.0 in MATH 136.
MATH 215 Study Abroad Mathematics 2 (1-10, max. 15): Mathematics courses taken through a UW approved study abroad program.
MATH 224 Advanced Multivariable Calculus (4): Topics include double and triple integrals, the chain rule, vector fields, line and surface integrals. Culminates in the theorems of Green and Stokes, along with the Divergence Theorem. Course overlaps with: TMATH 224. Prerequisite: a minimum grade of 2.0 in either MATH 126 or MATH 136.
MATH 282 Exploring Opportunities in the Mathematical Sciences (1): Topics include finding a community; diversity and equity issues in STEM and the mathematical sciences; academic planning; navigating academic support services; undergraduate research; graduate school; careers in the mathematical sciences. For students interested in careers in the mathematical sciences. Credit does not apply toward a mathematics major or an applied and computational mathematical sciences major at UW Seattle.
MATH 300 Introduction to Mathematical Reasoning (4): Mathematical arguments and the writing of proofs in an elementary setting. Elementary set theory, elementary examples of functions and operations on functions, the principle of induction, counting, elementary number theory, elementary combinatorics, recurrence relations. Prerequisite: a minimum grade of 2.0 in either MATH 126 or MATH 136.
MATH 301 Elementary Number Theory (4): Brief introduction to some of the fundamental ideas of elementary number theory.
MATH 315 Study Abroad Mathematics 3 (1-10, max. 15): Mathematics courses taken through a UW approved study abroad program.
MATH 318 Advanced Linear Algebra Tools and Applications (4): Eigenvalues, eigenvectors, and diagonalization of matrices: nonnegative, symmetric, and positive semidefinite matrices. Orthogonality, singular value decomposition, complex matrices, infinite dimensional vector spaces, and vector spaces over finite fields. Applications to spectral graph theory, rankings, error correcting codes, linear regression, Fourier transforms, principal component analysis, and solving univariate polynomial equations.
MATH 327 Introductory Real Analysis I (4): Covers number systems, fields, order, the least upper bound property, sequences, limits, liminf and limsup, series, convergence tests, alternating series, absolute convergence, re-arrangements of series, continuous functions of a real variable, and uniform continuity. Course overlaps with: STMATH 424 and TMATH 424. Prerequisite: a minimum grade of 2.0 in either MATH 300 or MATH 334.
MATH 334 Accelerated [Honors] Advanced Calculus (5): Introduction to proofs and rigor; uniform convergence, Fourier series and partial differential equations, vector calculus, complex variables. Second year of an accelerated two-year sequence; prepares students for senior-level mathematics courses. Prerequisite: either a minimum grade of 2.0 in MATH 136, or a minimum grade of 3.0 in MATH 126 and a minimum grade of 3.0 in either MATH 207 or MATH 307 and a minimum grade of 3.0 in either MATH 208 or MATH 308.
MATH 335 Accelerated [Honors] Advanced Calculus (5): Introduction to proofs and rigor; uniform convergence, Fourier series and partial differential equations, vector calculus, complex variables. Second year of an accelerated two-year sequence; prepares students for senior-level mathematics courses. Prerequisite: a minimum grade of 2.0 in MATH 334.
MATH 336 Accelerated [Honors] Advanced Calculus (5): Introduction to proofs and rigor; uniform convergence, Fourier series and partial differential equations, vector calculus, complex variables. Second year of an accelerated two-year sequence; prepares students for senior-level mathematics courses. Prerequisite: a minimum grade of 2.0 in MATH 335.
MATH 340 Abstract Linear Algebra (4): Linear algebra from a theoretical point of view. Abstract vector spaces and linear transformations, bases and linear independence, matrix representations, Jordan canonical form, linear functionals, dual space, bilinear forms and inner product spaces. Course overlaps with: STMATH 409.
MATH 342 Art of Problem Solving (4): Explores the artful side of problem-solving, with examples from various fields across mathematics, including combinatorics, number theory, algebra, geometry, probability, and analysis.
**MATH 380 Intermediate Topics in Undergraduate Mathematics (3-5, max.
MATH 381 Discrete Mathematical Modeling (4): Introduction to methods of discrete mathematics, including topics from graph theory, network flows, and combinatorics. Emphasis on these tools to formulate models and solve problems arising in variety of applications, such as computer science, biology, and management science. Course overlaps with: STMATH 381. Prerequisite: a minimum grade of 2.0 in either CSE 121, CSE 122, CSE 123, CSE 142, CSE 143, or AMATH 301; and a minimum grade of 2.0 in either MATH 136 or MATH 208.
MATH 382 Careers in Mathematical Sciences (1): Preparation for careers in the mathematical sciences. Focuses on identification of key skills; creating an effective resume; articulating interests and experiences; doing informational interviews; and demonstrating professional communication. Credit does not apply toward a mathematics major or an applied and computational mathematical sciences major at UW Seattle.
MATH 394 Probability I (4): Axiomatic definitions of probability; random variables; conditional probability and Bayes' theorem; expectations and variance; named distributions: binomial, geometric, Poisson, uniform (discrete and continuous), normal and exponential; normal and Poisson approximations to binomial. Transformations of a single random variable. Markov and Chebyshev's inequality. Weak law of large numbers for finite variance. Course overlaps with: E E 391; STMATH 392; and TMATH 393. Prerequisite: either a minimum grade of 2.0 in MATH 126, or a minimum grade of 2.0 in MATH 136.
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