TEACHING Summary: My Teaching Statement in pdf format. Current Course Spring 2007: Math 139 Topics in Knot Theory Previous courses at Harvard: Math 134 Calculus on Manifolds (Fall 2004, Fall 2006) Introduction to manifolds in real n-space, inverse and implicit function theorems, differential forms, the general version of Stokes's Theorem, etc. Math 25b Honors Multivariable Calculus and Linear Algebra (Spring 2006) This course is a continuation from Math 25a. Topics covered include real analysis, multivariable calculus, differential forms and manifolds (if time permits). Math 25a Honors Multivariable Calculus and Linear Algebra (Fall 2005) A rigorous treatment of linear algebra, point-set and metric topology. Emphasis placed on careful reasoning, and on learning to understand and construct proofs. Math 21b Linear Algebra (Spring 2005, Fall 2006) Math 21a Multivariable Calculus (Fall 2004) While at the University of Illinois: Math 135 Calculus I (Spring 2000) Math 130 Calculus II (Fall 1998, Spring 1999, Fall 1999) Math 242 Multivariable Calculus (Fall 2000, Fall 2001, Fall 2002) This was taught at Unit One Allen Hall, a program which provides students with a small liberal arts college environment within the wider community at the University of Illinois at Urbana-Champaign. For more information about Allen Hall click here. C&M 242 Multivariable calculus (Spring 2001) The third course in calculus and analytic geometry taught with active learning techniques using Calculus & Mathematica. Click here for more information. As an undergraduate at the University of Sydney: Recitation instructor for an Introductory Linear Algebra course. Grader for Freshman Calculus courses, Introductory Topology course and for the correspondence program for the Australian Mathematics Olympiad Committee. I have also twice been a tutor at the Australian National Mathematics Summer School. Teaching Awards and Recognition: Fall 2004: CUE (Course Evaluation) guide Harvard University. Received "special recognition for teaching abilities" for multivariable calculus. Recognition based on student evaluations. Spring 2002: LAS Award for Excellence in Undergraduate Teaching University of Illinois, Urbana-Champaign. (Awarded to 6 out of 1000 Liberal Arts and Sciences College Teaching Assistants each year.) May 2000: Mathematics Instructional Award for excellence in teaching at the University of Illinois, Urbana-Champaign. Placed on Incomplete List for Excellent Teachers University of Illinois, Urbana-Champaign: Spring 1999, Fall 1999, Spring 2000, Fall 2000, Spring 2001, Fall 2001, Fall 2002. (Awarded to top 10% of instructors across the UIUC campus based on student evaluations of instructor effectiveness.) Research Experiences for Undergraduates: Summer 2005: Gerardo Con Diaz's project included a study of the supercrossing number of knots. Harvard University. Summer 2004: Gerardo Con Diaz's project included an introduction to knot theory, seifert surfaces, signature of a knot and proving that (2,2n+1) torus knots have signature 2n for any integer n. Harvard University. Summer 2001 and 2002: I was an associate mentor for both illiMath2001 REU and the illiMath2002 REU - Research Experience for Undergraduates at the University of Illinois, Urbana-Champaign. Click HERE for a Java applet which explores the Crossing Map of a knot (developed at illiMath2002). Other teaching experiences: Spring 2002: Chair Teaching Assistant Teaching Awards Committee, University of Illinois, Urbana-Champaign. Spring 2001: Student Representative Teaching Assistant Teaching Awards Committee, University of Illinois, Urbana-Champaign. Fall 2000 and Spring 2001: Mentor Teaching Assistant Training Program, University of Illinois, Urbana-Champaign. Aug. 2000 and 2001 Student Assistant Teaching Assistant Orientation, University of Illinois, Urbana-Champaign.