Possible Course Project TopicsMA 330 002, Spring 2012Below is a list of possible course project topics. You are not restrictedto completing a project from this list. For each topic, I have listed a math-ematical topic and a person who was heavily involved in that topic whomight be of interest for biographical reasons. Not all of these topics are ap-propriate for all students; an appropriate choice of topics depends on yourmathematical background.(1) The Erd˝os-Ko-Rado Theorem: Erd˝os (combinatorics)(2) Galois’ Theorem regarding solvability of polynomials by radicals:Galois (classical and modern algebra)(3) Abel’s Theorem regarding the unsolvability of the quintic by radicals:Abel (classical algebra)(4) Quadratic Reciprocity: Gauss (elementary number theory)(5) Fundamental Theorem of Algebra: Euler, Gauss (classical algebra)(6) Hilbert’s Third Problem: Hilbert, Dehn (geometry)(7) Brouwer Fixed Point Theorem: Brouwer (topology)(8) The Cayley-Hamilton Theorem: Cayley (linear algebra)(9) Lagrange’s Theorem for finite subgroups of a finite group: Lagrange(modern algebra)(10) Stirling’s Formula: Stirling (calculus and advanced calculus)(11) Irrationality of π: various mathematicians (calculus)(12) Hyperbolic Geometry: Poincar`e (geometry)(13) Partition Identities: Ramanujan, Percy MacMahon (combinatorics,number theory)(14) Noether Isomorphism Theorems: Emmy Noether (modern algebra)(15) Fourier Series: Fourier (calculus)(16) Calculating Machines: Pascal, Leibnitz, Babbage (computer science)(17) Infinite Series: Newton, Maclaurin, Taylor (calculus)(18) Partial Differential Equations (wave equation, heat equation): d’Alembert(calculus)(19) Five Color Theorem: Kempe, Heawood (combinatorics)(20) Cayley’s Tree Theorem: Cayley, Pl¨ucker (combinatorics)(21) Catalan Numbers: Catalan (combinatorics)(22) Transcendental nature of e: Hermite (analysis)(23) Pell’s Equation: Diophantus, Lagrange (number theory)(24) Euler’s totient function and encryption schemes: various mathemati-cians (number theory)(25) Least squares methods and linear regression: Gauss (linear algebra)(26) Magic Squares: Stanley, MacMahon, many others (combinatorics,recreational mathematics)(27) Classification of Plane Symmetry Groups: Da Vinci (abstract alge-bra, art)12(28) Bernoulli Polynomials and Bernoulli Numbers: various mathemati-cians (combinatorics, number theory, analysis)(29) Eulerian Numbers: Euler, MacMahon (combinatorics, number the-ory)(30) Historical Development of the Integral: Archimedes, Newton, Leib-niz, Cauchy, Riemann, Lebesgue (calculus, analysis)(31) Non-Euclidean Geometry: Bolyai, Gauss, Lobachevsky, others (ge-ometry)(32) Solutions to cubic and quartic equations: Cardano, Tartaglia, manyothers (classical algebra)(33) Fibonacci numbers and the golden ratio: various mathematicians(number theory,