Nathan Kaplan

nckaplan@math.uci.edu


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Courses at UC Irvine

Fall 2017

Math 232a: Algebraic Number Theory

The first quarter of the year-long graduate algebraic number theory sequence.
Textbooks: D. Marcus, Number Fields
J. Neukirch, Algebraic Number Theory

Math 3a: Introduction to Linear Algebra

An introduction to linear algebra.
Textbook: D. Lay, S. Lay and J. McDonald, Linear Algbera and its Applications, 5th ed.

Spring 2017

Math 3a: Introduction to Linear Algebra

An introduction to linear algebra. (Two sections)
Textbook: D. Lay, S. Lay and J. McDonald, Linear Algbera and its Applications, 5th ed.
The syllabus is available here.

Winter 2017

Math 175: Combinatorics

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.
The syllabus is available here.

Fall 2016

Math 233a: Algebraic Geometry

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

Winter 2016

Math 230b: Algebra

The second quarter of the year-long graduate algebra sequence.
Textbook: D. Dummit and R. Foote, Abstract Algebra
The syllabus is available here.

Math 120a: Group Theory

A proof-based introduction to abstract algebra.
Textbook: J. Fraleigh, A First Course in Abstract Algebra, Seventh Edition
The syllabus is available here.

Fall 2015

Math 230a: Algebra

The first quarter of the year-long graduate algebra sequence.
Textbook: D. Dummit and R. Foote, Abstract Algebra
The syllabus is available here.

Courses at Yale

Spring 2015

Math 354: Number Theory

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.

Math 719: Asymptotic Problems in Number Theory

A graduate topics class focusing on class groups of number fields and rational points on curves over finite fields.
There was no textbook.  The syllabus is available here. A summary of the lectures is here.

Fall 2014

MATH 244: Discrete Mathematics

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

MATH 766: Elliptic Curves

Graduate course on the arithmetic theory of elliptic curves building towards a proof of the Mordell-Weil theorem.
Textbook: Silverman, The Arithmetic of Elliptic Curves
The syllabus is available here.

Fall 2013

MATH 244: Discrete Mathematics

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

MATH 120: Multivariable Calculus

Textbook: Stewart, Multivariable Calculus Early Transcendentals, Math 120

Courses at Harvard

Spring 2013

Math 21b: Linear Algebra and Differential Equations

Textbook: Bretscher, Linear Algebra with Applications

Fall 2012

Math 1a: Introduction to Functions and Calculus I (Graduate Course Fellow)

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

Spring 2011 and Fall 2010

EMR 23: Fat Chance (Head Teaching Fellow)

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: Gross and Harris, The Magic of Numbers (plus additional course notes)

Summer 2011

Coding Theory (Summer Tutorial)

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.