LaTex Installation:  TexShop for Mac  •  MikTex for PC • latex source example • latexed pdf of example source file • latex slides example • latexed pdf of slide example

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Examples of mathematical writing:

• Steven Strogatz  ''Elements of Mathematics''
• Eugene Wigner   ''The unreasonable effectiveness of mathematics in the natural sciences''
• Paul Lockhart     ''A Mathematician's Lament" (specially recommended for anyone who wants to teach mathematics)
• Robert Kanigel    "The Man Who Knew Infinity: A Life of the Genius Ramanujan"
• G. H. Hardy         "A Mathematician's Apology"
• Simon Singh       "Fermat's Last Theorem"
• Timothy Gowers  "Mathematics. A Very Short Introduction"
  
• Donal O'shea       "The Poincare Conjecture"
• Edward Frenkel    "Love and Math"
  

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Umass Library
UMass Writing Center:  tutoring and advise on your writing.
UMass Career Center:  advise on job applications, internships, grad school applications, cover letters, vitae.

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The main objective of this class is to practice writing about mathematics. We will also write a cover letter and vita for possible job/internship/grad school applications. All write ups should be done in the word processing system LaTex.  The mathematical writing will be based on

• General audience lectures given by famous mathematicians on various topics. Your assignment will be to write an overview of the lectures, or inject some of your own views on the addressed topics etc.
• Chapters from the books by Donal O'shea  "The Poincare Conjecture" and Edward Frenkel "Love and Math".
• A selection of the 2000 millenium price problems (Poincare conjecture, Riemann Hypothesis, Birch Swinnerton-Dyer conjecture) which you will be presenting in group projects.

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Group Projects

Diophantine equations 1:  Lukianov, Mellow, Santana, Chi, Dahl
Conic sections, Pythagorean triples, congruent number problem.

Diophantine equations 2:  Petrangelo, Tri Pham, Justin Pham, Choi, Piseth Chhoeuy
Elliptic curves, Weierstrass normal form, their shapes in the real plane.

Diophantine equations 3:  Lassalle, Rodriguez, Weng, Jiabao Shang
Elliptic curves as abelian group, abelian group of rational points, Mordell's theorem and rank, Birch and Swinnerton-Dyer conjecture.

Elliptic curves and doughnuts: Prescott, Shen, Smith, Bhavjit Thiara
Elliptic curves and Weierstrass P-function, Abel-Jacobi map, circumference of ellipse, Pendulum ODE.

Prime numbers 1: Uhlig, Abdulla, Smolak, Doyle, Yu
Primes, unique factorization, Euclid's proof for the infinity of primes, famous conjectures about primes.

Prime numbers 2: Scholick, Gelber, Qu, Riemer
Distribution of primes, Riemann zeta function, Euler product presentation, alternative proof for the infinity of primes, Riemann hypothesis

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Schedule

9/8: overview of class obejctives and first assignment: one page single spaced essay on "Why did I choose mathematics as my subject of studies?" Due 9/15.

9/10: listen to and briefly discuss the keynote address of Timothy Gowers on ''The Importance of Mathematics''.

9/15: "Why did I choose mathematics ..." hand in date. Discuss Gowers' arguments, perhaps expand some of his
          math examples. Latex tutorial.
         Second assignment: summarize Gowers' lecture in an at least 1 1/2 page single spaced paper. Due 9/24.

9/17:  Diophantine equations (Fermat's Last Theorem), shapes of surfaces, and theoretical physics: a very
          impressionistic view I.

9/22:  Diophantine equations (Fermat's Last Theorem), shapes of surfaces, and theoretical physics: a very
         impressionistic view II.

9/24: Presentation by Tommie Joyner Jr., Assistant Director for Career Planning, Career Services Umass, on
        resume  and cover letter writing.
           Gowers' lecture paper due.

9/29: Diophantine equations (Fermat's Last Theorem), shapes of surfaces, and theoretical physics: a very
         impressionistic view III.

10/01: Umass Writing Center presentation approx. 10-15 minutes. Fermat's Last Theorem video by Simon Singh.

10/06: Group project assignments. Introdcution to primes, the prime counting function and the RIeman zeta function I.
          Due date for essay on "Fermat's Last Theorem".

10/08: Introdcution to primes, the prime counting function and the RIeman zeta function II. Millenium prize lecture
          by Tate on the Riemann hypothesis and the Birch & Swinnerton-Dyer conjecture.

10/15: Umass Library presentation, Paulina Borrego Science & Engineering Librarian:
          appropriate resources effectively, citation management, and plagiarism issues.

10/20: From equations to zeta-like functions I. Due date for resume and cover letter.

10/22: From equations to zeta-like functions II.

10/27: Elliptic curves, Mordell's Theorem, Birch and Swinnerton-Dyer conjecture.
         
10/29: Millenium prize lecture by Tate on the Birch  & Swinnerton-Dyer conjecture.
          Due date for paper ''2 poofs of the infinitudes of primes''.

11/03: Group 1 starts presenting.

11/05: Group 1 finishes.

11/10: Group 2 starts presenting.

11/12: Group 2 finishes.

11/17: Group 3 starts presenting.

11/19: Group 3 finishes.

11/24: Group 4 starts presenting.