50 Weeks of Mathematics

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

– Karl Friedrich Gauss

Completely disregarding Gauss’ sage advice, I commit to “sketching” (see my previous blog post: The Importance of Sketching) 50 Mathematical Topics in 50 weeks for your reading pleasure.

A sketch of the proposed topics are as follows:

Sunday 29 March 2015 Week 1 Set Theory
Sunday 5 April 2015 Week 2 Mathematical Logic
Sunday 12 April 2015 Week 3 How to Prove It – Mathematical Proof
Sunday 19 April 2015 Week 4 Single Variable Calculus
Sunday 26 April 2015 Week 5 Linear Algebra I
Sunday 3 May 2015 Week 6 Linear Algebra II
Sunday 10 May 2015 Week 7 Multi variable Calculus I
Sunday 17 May 2015 Week 8 Multi variable Calculus II
Sunday 24 May 2015 Week 9 An Introduction to Probability
Sunday 31 May 2015 Week 10 Computability Theory
Sunday 7 June 2015 Week 11 Group Theory
Sunday 14 June 2015 Week 12 Graph Theory
Sunday 21 June 2015 Week 13 Euclidean Geometry
Sunday 28 June 2015 Week 14 Analysis I
Sunday 5 July 2015 Week 15 Analysis II
Sunday 12 July 2015 Week 16 Analysis III
Sunday 19 July 2015 Week 17 Elementary Number Theory I
Sunday 26 July 2015 Week 18 Elementary Number Theory II
Sunday 2 August 2015 Week 19 Abstract Algebra – Rings and Fields
Sunday 9 August 2015 Week 20 Abstract Algebra – Vector Spaces and Modules
Sunday 16 August 2015 Week 21 Abstract Algebra – Galois Theory
Sunday 23 August 2015 Week 22 Topology I
Sunday 30 August 2015 Week 23 Topology II
Sunday 6 September 2015 Week 24 Complex Analysis I
Sunday 13 September 2015 Week 25 Complex Analysis II
Sunday 20 September 2015 Week 26 Ordinary Differential Equations
Sunday 27 September 2015 Week 27 Partial Differential Equations
Sunday 4 October 2015 Week 28 Measure Theory
Sunday 11 October 2015 Week 29 Statistics: A Crash Course I
Sunday 18 October 2015 Week 30 Statistics: A Crash Course II
Sunday 25 October 2015 Week 31 Electrodynamics
Sunday 1 November 2015 Week 32 An Introduction to Quantum Mechanics
Sunday 8 November 2015 Week 33 Special Relativity
Sunday 15 November 2015 Week 34 General Relativity
Sunday 22 November 2015 Week 35 Combinatorics
Sunday 29 November 2015 Week 36 Gödel’s Theorems
Sunday 6 December 2015 Week 37 Functional Analysis I
Sunday 13 December 2015 Week 38 Functional Analysis II
Sunday 20 December 2015 Week 39 Algebraic Geometry
Sunday 27 December 2015 Week 40 Algebraic Topology
Sunday 3 January 2016 Week 41 Algorithmics
Sunday 10 January 2016 Week 42 Calculus of Variations
Sunday 17 January 2016 Week 43 Elementary Fluid Dynamics
Sunday 24 January 2016 Week 44 Computational Complexity I
Sunday 31 January 2016 Week 45 Computational Complexity II
Sunday 7 February 2016 Week 46 Machine Learning I
Sunday 14 February 2016 Week 47 Machine Learning II
Sunday 21 February 2016 Week 48 Stochastic Processes
Sunday 28 February 2016 Week 49 Elementary Numerical Analysis
Sunday 6 March 2016 Week 50 Looking Back and Looking Forward

Well I am committed now. Watch this space …


Some useful Resources in compiling this sketch:

http://www.maths.cam.ac.uk/undergrad/course/

https://www.math.ucla.edu/ugrad/courses

http://www.ox.ac.uk/admissions/undergraduate/courses-listing/mathematics

http://en.wikipedia.org/wiki/Areas_of_mathematics


The End

Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand – and it always turned out that understanding was all that mattered.

– Alexander Grothendieck

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3 Responses to 50 Weeks of Mathematics

  1. Chow Kim Wan says:

    Hi!

    I look forward to seeing your updates on math!

    Like

    • Chow Kim Wan says:

      What’s your favorite topic? Mine will be algebra (not the one in high school, I mean algebraic structures like groups and rings).

      Like

      • I hope to stick to the rather demanding schedule … we will see.

        Picking up on your favourite, I think one of my favourite weeks will be when we use the concepts from group theory and field theory etc. and extend them and look at Galois Theory, in particular as it applies to the Abel–Ruffini theorem.

        There are many others, my particular favourites will be Godel’s Theorems, Computational Complexity and I have a particular fondness for Graph Theory.

        I am looking forward to composing all the posts however.

        Like

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