Nathan Kaplan

A year-long graduate algebraic number theory sequence.

The primary reference for the Fall quarter will be course notes of Matt Baker: Algebraic Number Theory.

Textbook: J. Silverman, A Friendly Introduction to Number Theory.

Textbook: J. Silverman, A Friendly Introduction to Number Theory.

Textbook: J. Silverman, A Friendly Introduction to Number Theory.

Textbook: J. Silverman, A Friendly Introduction to Number Theory.

Textbook: D. Dummit and R. Foote, Abstract Algebra.

Textbook: D. Dummit and R. Foote, Abstract Algebra.

Textbook: D. Dummit and R. Foote, Abstract Algebra.

An introduction to Integral Calculus.

Textbook: J. Stewart, Calculus: Early Transcendentals, 8th Edition.

The syllabus from the Spring 2020 offering of the course is available here.  This offering of the course was taught remotely because of COVID-19.

The lecture videos for this course are available at my YouTube channel 'nckaplan math'.

A proof-based introduction to abstract algebra.

Textbook: J. Fraleigh, A First Course in Abstract Algebra, Seventh Edition.

A recent version of the syllabus is available here.

A proof-based introduction to combinatorics.

Textbooks: L. Lovász, J. Pelikán, K. Vesztergombi, Discrete Mathematics: Elementary and Beyond.
J. Harris, J. Hirst and M. Mossinghoff, Combinatorics and Graph Theory, 2nd ed.

A recent version of the syllabus is available here.

An introduction to linear algebra.

Textbook: D. Lay, S. Lay and J. McDonald, Linear Algebra and its Applications, 5th ed.

A recent version of the syllabus is available here.

A year-long graduate algebraic number theory sequence.

Textbooks: D. Marcus, Number Fields and J-.P. Serre, A Course in Arithmetic.

Course Notes: M. Baker, Algebraic Number Theory and P. Stevenhagen, Number Rings.

The syllabi are available here: 232a, 232b, 232c.

The first quarter of the year-long graduate algebraic geometry sequence.

Textbook: I. Shafarevich, Basic Algebraic Geometry I.

The syllabus is available here.

The first two quarters of the year-long graduate algebra sequence.

Textbook: D. Dummit and R. Foote, Abstract Algebra.

The syllabi are available here: 230a, 230b.

A proof-based number theory course with a semester of abstract algebra as a prerequisite.

Textbook: K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory.

The syllabus is available here. A summary of the lectures is here.

A graduate topics class focusing on class groups of number fields and rational points on curves over finite fields.

The syllabus is available here. A summary of the lectures is here.

A proof-based introduction to combinatorics and graph theory.

Textbooks: L. Lovász, J. Pelikán, K. Vesztergombi, Discrete Mathematics: Elementary and Beyond.
J. Matoušek and J. Nešetřil, An Invitation to Discrete Mathematics.

The syllabus is available here. A summary of the lectures is here.

Graduate course on the arithmetic theory of elliptic curves building towards a proof of the Mordell-Weil theorem.

Textbook: J. Silverman, The Arithmetic of Elliptic Curves.

The syllabus is available here.

Textbook: J. Stewart, Multivariable Calculus Early Transcendentals, Math 120.

Textbook: O. Bretscher, Linear Algebra with Applications.

Textbook: R. Gottlieb, Calculus: An Integrated Approach to Functions and Their Rates of Change.

I served as the head teaching fellow for a new introductory probability and statistics course in Harvard's general education program taught by Dick Gross and Joe Harris.

Textbook: D. Gross and J. Harris, The Magic of Numbers (plus additional course notes).