This page consists of all lecture notes and handouts related to lectures given at the 2014-2015 Advanced Solving Group at the Fields' Institute Math Circle. Solutions to handout problems/exercises will be uploaded shortly after postings of notes.
Analysis Lecture Series #1:
1. Foundational Aspects of Real Analysis and Cardinality:
2. Sequences, Convergence and Continuity
3. Connectedness, Compactness, Convexity; Differentiation and the Mean Value Theorem
In fact, I drafted an almost complete set of course notes called Real Analysis for Problem Solvers.
In the winter of 2015 I mentored Toronto area high-school students in regards to problems related to exponential sums and equidistribution. Here are some handouts that came out of this:
1. Proof Techniques (Induction, Pigeonhole Principle)
2. Complex Numbers and Basic Exponential Sums
3. Equidistribution of Sequences
(Disclaimer: All content in these notes, including theorem statements, proofs, solutions etc., unless otherwise stated, are my own product. I therefore claim responsibility for any errors that might be found in these notes.)
Suggested Problem Books related to some of the topics in these series:
1. Putnam and Beyond by T. Andreescu and R. Gelca.
2. Problem Solving Through Problems by L. Larson.
3. Berkeley Problems in Mathematics by P.N. de Souza and J.N. Silva.
I have been asked to offer my perspectives about careers for people who are mathematically oriented. If this interests you, take a look at this note.