Indiana University–Purdue University Indianapolis:
  • 674/693 — Mathematical Physics II/Topics in Analysis
    • (S16) — A Course on Orthogonal Polynomials [evals]
    • (S18) — Logarithmic Potential Theory
    • (S23) — Classical Approximation Theory on an Interval [evals]
  • 545 (S24) — Real Analysis and Measure Theory II
  • 544 (F22,F23) — Real Analysis and Measure Theory [evals 1] [evals 2]
  • 531 (F15) — Functions of Complex Variable II (A Course on Algebraic Functions) [evals]
  • 530 (S15,S20) — Functions of Complex Variable I [syllabus]
    [x]

    Textbook: Complex Analysis by Lars Ahlfors, 3rd edition

    This course covers Sections 1.1—1.2, 2.1—2.3, 3.2—2.3, 4.1—4.6, 5.1—5.3, 5.5, and 6.1 of Ahlfors’ book. It contains the material necessary for passing the Qualifying Exam in Complex Analysis for PhD students at IUPUI.

    [evals 1] [evals 2]
  • 445 (F21) — Foundations of Analysis II [evals]
  • 444 (F20) — Foundations of Analysis I [evals]
  • 425/525 (F17,F19,F20,F22,F23) — Elements of Complex Analysis [evals 1] [evals 2] [evals 3] [evals 4] [evals 5]
  • 351 (F18,S19,F19) — Introduction to Linear Algebra [syllabus]
    [x]

    Textbook: Linear Algebra by Howard Anton, 11th edition

    This course covers Chapters 1-6. It uncludes the following topics: Systems of linear equations, matrices, vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and applications.

    [evals 1] [evals 2] [evals 3]
  • 300 (F14,F15,S19) — Logic and the Foundations of Algebra [syllabus]
    [x]

    Textbook: Reading, Writing, and Proving by Daepp and Gorkin, 2nd edition

    3 credits, Chapters 1—24 (some chapters will be omitted). The core material for this course is drawn from basic set theory with the ultimate goal of learning how to compare sizes of different infinite sets. The material provides you with good foundation for courses in abstract algebra and real analysis. In spirit, the course is designed to help you bridge the gap between elementary and advanced courses in mathematics, move from solving problems to rigorously proving mathematical statements.

    [evals 1] [evals 2] [evals 3]
  • 276 (S17,S22) — Discrete Mathematics [syllabus]
    [x]

    Textbook: Discrete Mathematics (Elementary and Beyond) by Lovász, Pelikán, and Vesztergombi

    3 credits, Chapters 1—13 and 15. The class includes the following topics: Basic Logic, Counting and Induction, Discrete Probability, Integer Algorithms, and Graph Theory.

    [evals 1] [evals 2]
  • 266 (F14,S16,S17,Su18,S20,Su20,S21,S23) — Ordinary Differential Equations [syllabus]
    [x]

    Textbook: Differential Equations by Blanchard, Devaney, and Hall, 4th edition (primary text)
          Diffy Qs by J. Lebl, version 6.0 (secondary text, open source, can be found here)

    3 credits, Chapters 1—4 and 6 (some sections will be omitted). Many basic principles in physics, engineering, economics, and other fields are expressed mathematically in terms of equations involving a function of one variable and its derivatives. This goal of this course is to familiarize students with solution techniques for such equations and develop an intuition for solution properties. Applications of differential equations in mathematical models will be frequently discussed in the course. The class includes the following topics: first– and second–order differential equations; systems of first–order linear differential equations; qualitative analysis of solutions for differential equations; Laplace transforms; numerical methods.

    [evals 1] [evals 2] [evals 3] [evals 4] [evals 5] [evals 6] [evals 7] [evals 8]
  • 232 (Su23) — Calculus for Life Sciences II [evals]
  • 166 (S14,S18,F18) — Analytic Geometry and Calculus II [syllabus]
    [x]

    Textbook: Multivariable Calculus by James Stewart, 7th edition

    This is the second course in a 4–course sequence for Math, Science, and Engineering majors (MATH 16500 — 16600 — 17100 — 26100). This course is equivalent to IU MATH M216. Topics include transcendental functions, techniques of integration, indeterminant forms and improper integrals, basic differential equations, polar coordinates, sequences, infinite series, and power series.

    [evals 1] [evals 2] [evals 3] [evals 4]
  • S165 (F17) — Honors Analytic Geometry and Calculus I [evals]
  • 165 (F13,Su19,S22,S24) — Analytic Geometry and Calculus I [syllabus]
    [x]

    Textbook: Calculus by James Stewart, 7th edition

    This is the first course in a 4–course sequence for Math, Science, and Engineering majors (MATH 16500 — 16600 — 17100 — 26100). This course is equivalent to PU MATH 16300 and IU MATH M215. Topics include plane analytic geometry and trigonometry, functions, limits, differentiation and applications, integration and applications, and the Fundamental Theorem of Calculus.

    [evals 1] [evals 2] [evals 3]

University of Oregon:
  • 619 (Spring 2012) Second Course in Complex Analysis — Potential Theory in the Complex Plane [evaluations]
  • 420 (Fall 2011, Fall 2012) — Ordinary Differential Equations [syllabus]
    [x]

    Textbook: Ordinary Differential Equations by M. Tenenbaum and H. Pollard;
    Ordinary Differential Equations by T. Myint–U (secondary)

    This course covers:
    • basic concepts: definition and solutions of ODEs; directional fields
    • special types of the first order ODEs: ODEs with separable variables; ODEs with homogeneous coefficients; exact ODEs; integrating factors
    • series method for the first order ODEs: Taylor series and convergence of series; linear ODEs; general first order ODEs
    • existence theorem: Picard’s approximations; convergence of sequences of functions • existence theorem; continuity theorem
    • higher order linear ODEs: basic facts; Laplace transform and Gamma function; linear ODEs with constant coefficient; reduction of order method; power series method at regular and singular regular points
    • systems of ODEs: basic facts; linear systems; exponential of a matrix; Jordan canonical form of a matrix; linear systems with constant coefficients; linear systems with periodic coefficients; stability of autonomous systems
    • physical problems leading to ODEs (independent study).

    [evaluations]
  • 282 (Spring 2011) — Second Quarter of Multivariate Calculus [syllabus]
    [x]

    Textbook: Multivariable Calculus by James Stewart, 6th edition

    This course continues the study of multivariable calculus and focuses on integration of functions of several variables. The course, which is the second in the sequence, covers Chapters 16 and 17 of Stewart.

    [evaluations]
  • 263 (Spring 2013) — Third Quarter of Calculus with Theory [syllabus]
    [x]

    Textbook: Calculus by Michael Spivak, 4th edition

    This course is third in the series of three and tentatively covers Chapters 20—30 of the book. The material includes application of the approximation by polynomials, infi- nite sequences and series, uniform convergence, basics of the complex function theory, and construction of real numbers.

    [evaluations]
  • 262 (Winter 2013) — Second Quarter of Calculus with Theory [syllabus]
    [x]

    Textbook: Calculus by Michael Spivak, 4th edition

    This course is first in the series of three and tentatively covers Chapters 11—19 of the book. The material includes application of the differentiation, inverse functions, trigonometric, exponential and logarithmic functions, and the theory of integration.

    [evaluations]
  • 261 (Fall 2012) — First Quarter of Calculus with Theory [syllabus]
    [x]

    Textbook: Calculus by Michael Spivak, 4th edition

    This course is first in the series of three and tentatively covers Chapters 1—11 of the book. The material includes basic properties of numbers, definition and properties of functions, limits, continuity, properties of continuous functions, and differentiation.

    [evaluations]
  • 233 (Spring 2011) — Third Quarter of Discrete Mathematics [syllabus] [evaluations]
    [x]

    Textbook: Discrete and Combinatorial Mathematics by R.P. Grimaldi

    This course continues the introduction to the subject of discrete mathematics. Topics include: graphs and trees; optimization and matching; groups, rings, and fields. The course, which is the third in the sequence, covers most of Chapters 11—14 and parts of Chapters 16 and 17 of Grimaldi.

  • 232 (Winter 2011, Winter 2012) — Second Quarter of Discrete Mathematics [syllabus]
    [x]

    Textbook: Discrete and Combinatorial Mathematics by R.P. Grimaldi

    This course continues the introduction to the subject of discrete mathematics. Topics include: abstract theory of functions and relations; finite state machines; counting via the principle of inclusion and exclusion; counting via generating functions; first and second order linear recurrence relations. The course, which is the second in the sequence, covers most of Chapters 5—10 of Grimaldi.

    [evaluations]
  • 231 (Fall 2011, Fall 2010) — First Quarter of Discrete Mathematics [syllabus]
    [x]

    Textbook: Discrete and Combinatorial Mathematics by R.P. Grimaldi

    This course introduces students to the subject of discrete mathematics. Topics include: fundamental principles of combinatorics; elementary logic; basic set theory; introduction to discrete probability; integer arithmetic. The course, which is the first in the sequence, covers most of the first four chapters of Grimaldi.

    [evaluations]

Vanderbilt University:
  • 150B (Spring 2007, Spring 2005) — Second Semester of Beginners Calculus
  • 150A (Spring 2006, Fall 2004) — First Semester of Beginners Calculus