Splash Biography
CHIRAG BHARADWAJ, Junior computer engineer at Cornell University
Major: Computer Science College/Employer: Cornell Year of Graduation: 2017 

Brief Biographical Sketch:
Chirag Bharadwaj is from Flushing, NY and lived there until 2007. He is a senior at Cornell, and is currently 19 years old. Chirag has a history of teaching math at the high school level. He attended high school near Princeton, NJ, and during each of his four years of high school, he taught the AP Calculus curriculum in a classroom setting as a certified AP teacher to over twenty students after teaching himself calculus in the 8th grade. This in turn allowed his school district to run a better calculus program for the students. Almost every student under his tutelage received a score of 4 or higher on the AP exams in May, an amazing feat. More information (lessons, exams, etc.) about this nontraditional course can be found on his website. Chirag has taught things like Victorianera Polynomial Analysis, the Japanese Language, and Complex Analysis before at Splash. His interests lie in the intersection of various other fields as well. Chirag is resuming his old post as an abstract mathematics instructor this semester, but has decided to branch out and embrace some of its applications, including music theory. In the fall of 2016, Chirag will be teaching a basic introduction to music theory from the perspective of intermediatelevel math. Welcome aboard! Past Classes(Clicking a class title will bring you to the course's section of the corresponding course catalog)M316: Handy Techniques in Mathematics in Splash Spring 17 (Apr. 29, 2017)
This course will discuss various interesting proofs in advanced applied mathematics. We will learn about various important integrals, derivatives, and other interesting functions that are useful in various applied fields like atomic physics, physical chemistry, and quantum mechanics.
M257: Musical Groups: Exploring Music with Math in Splash Fall 2016 (Nov. 05, 2016  Apr. 29, 2017)
Groups are among some of the most interesting topics in modern mathematics. They have implications far beyond just the abstract; in this course, we will explore how groups in mathematics are at the very foundation of modern music. Here's a sample list of topics we might cover:
+ Basic abstract algebra (groups, sets, transformations, and geometric representations)
+ Music metatheory (intervals, temperaments, waves, frequency)
+ Music theory (transpositions, inversions, chords, arpeggios)
+ Relationships and connections between the two
+ Modern research about the two fields
If you're a music aficionado and want to learn more about the math behind why certain things work, this class is for you. You don't have to be a math whiz to understand why modern music works!
M203: Special Polynomials in Splash Spring 2016 (Apr. 23, 2016)
This class introduces some special polynomials used in mathematics. Students will learn about polynomial solutions to differential equations that have applications in physics and chemistry. The class provides a toolkit for differential equationsolving using Victorian algebraic techniques that anybody with an understanding of basic differential equations and a solid understanding of algebra can understand. We will not assume any knowledge other than strong algebra skills and knowledge of calculus of a single variable (including sequences and series).
H177: Introduction to Japanese Language and Culture in Splash Fall 2015 (Oct. 24, 2015)
A quick introduction to the Japanese language. Covers the following:
+ Writing systems
+ IPA
+ Romaji, hiragana, katakana, furigana
+ Some vocabulary
+ General phrases
If time permits, we will discuss aspects of Japanese culture as well.
M96: Introduction to Complex Analysis in Splash Spring 2015 (Apr. 18, 2015)
Based on a class for college sophomores/juniors. This is a rigorous introduction to complex analysis, with emphasis on developing a functional understanding of (half of) the subject. The pace is rapid, and we expect to cover the following topics:
+ Overview of complex numbers
+ Analytic functions
+ Cauchy's Theorem
+ Series representations
+ Residue analysis
Unfortunately, we will not have time to delve into conformal mappings or asymptotic methods. If this course is offered again next fall, it will cover the material that this course did not.
