## MATH 61DM: Modern Mathematics: Discrete Methods

This is the first part of a theoretical (i.e., proof-based) sequence in discrete mathematics and linear algebra. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments. The linear algebra content is covered jointly with
Math 61CM. Students should have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BC-level Advanced Placement calculus exam, or consent of the instructor.nnThis sequence is not appropriate for students planning to major in natural sciences, economics, or engineering, but is suitable for majors in any other field (such as MCS ("data science"), computer science, and mathematics).

Terms: Aut
| Units: 5
| UG Reqs: WAY-FR

Instructors:
Fox, J. (PI)
;
Devadas, S. (TA)

## MATH 62DM: Modern Mathematics: Discrete Methods

This is the second part of a proof-based sequence in discrete mathematics. This course covers topics in elementary number theory, group theory, and discrete Fourier analysis. For example, we'll discuss the basic examples of abelian groups arising from congruences in elementary number theory, as well as the non-abelian symmetric group of permutations. Prerequisites: 61DM or 61CM.

Terms: Win
| Units: 5
| UG Reqs: WAY-FR

Instructors:
Soundararajan, K. (PI)

## MATH 63DM: Modern Mathematics: Discrete Methods

Third part of a proof-based sequence in discrete mathematics. This course covers several topics in probability (random variables, independence and correlation, concentration bounds, the central limit theorem) and topology (metric spaces, point-set topology, continuous maps, compactness, Brouwer's fixed point and the Borsuk-Ulam theorem), with some applications in combinatorics. Prerequisites: 61DM or 61CM

Terms: Spr
| Units: 5
| UG Reqs: WAY-FR

Instructors:
Tokieda, T. (PI)
;
Bates, E. (TA)

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