teaching

Math 180B: Number Theory
Textbook: J. Silverman, A Friendly Introduction to Number Theory.

Winter 2024

Math 180A: Number Theory
Textbook: J. Silverman, A Friendly Introduction to Number Theory.

Winter 2023

Math 230B: Algebra (Graduate Course)
Textbook: D. Dummit and R. Foote, Abstract Algebra.

Fall 2022

Math 230A: Algebra (Graduate Course)
Textbook: D. Dummit and R. Foote, Abstract Algebra.

Fall 2020, Winter 2021, Spring 2021

Math 206ABC: Algebra (Graduate Course)
Textbook: D. Dummit and R. Foote, Abstract Algebra.

Here is a page containing materials that I created for these courses including links to lecture videos on YouTube. I hope that these materials will be useful for students taking similar courses and for students preparing for the Algebra Qualifying Exam.

Fall 2019, Winter 2020, Spring 2020, Summer 2020

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'.

Winter 2019, Fall 2018, Winter 2016

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.

Winter 2018, Winter 2017

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.

Fall 2017, Spring 2017

An introduction to linear algebra.
Textbook: D. Lay, S. Lay and J. McDonald, Linear Algbera and its Applications, 5th ed.
A recent version of the syllabus is available here.

Fall 2017, Winter 2018, Spring 2018

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.

Fall 2016

The first quarter of the year-long graduate algebraic geometry sequence.
Textbook: I. Shafarevich, Basic Algebraic Geometry I.
The syllabus is available here.

Fall 2015, Winter 2016

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.

Courses at Yale

Spring 2015

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.

Fall 2014, Fall 2013

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.

Spring 2014

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.

Fall 2013

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

Courses at Harvard

Spring 2013

Fall 2012

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

Spring 2011 and Fall 2010

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).

Summer 2011

I taught a six week summer tutorial on the mathematical theory of error-correcting codes. Together with the student participants I created course notes available here.

Nathan Kaplan

nckaplan@math.uci.edu

I am happy to share materials from the courses I have taught. Please email me if you are interested.

Courses at UC Irvine

Spring 2024