2011/09/23/welcome-to-the-cambridge-mathematical-tripos

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*1. Mathematics becomes hard.* Every mathematician will be able to
tell you rather precisely when it was that they found that mathematics had
stopped being an easy subject.

*2. When the going gets tough, it is not some failing of yours.* It
simply means that, just like everybody else, you have to *work*.
Unhelpful thing to say if it is not backed up with instructions about *how*
to work.

*how to come up with relatively routine proofs*. To elaborate a
little, there are a lot of arguments in mathematics that experienced
mathematicians find very easy to think of, but beginners find much more
difficult. What is it about the brains of experts that makes them find it so
much easier? How can you convert your brain into that kind of brain? That is
what I want to try to explain.

photoplethysmography

to know heart-rate information when you're working out and throughout the day

With a little bit of practice one can make basic logical deductions completely mechanically, and it is absolutely essential to learn how to do so.

- 2011/09/25/basic-logic-connectives-and-and-or
- 2011/09/26/basic-logic-connectives-not
- 2011/09/28/basic-logic-connectives-implies
- 2011/09/30/basic-logic-quantifiers
- 2011/10/02/basic-logic-relationships-between-statements-negation
- 2011/10/05/basic-logic-relationships-between-statements-converses-and-contrapositives
- 2011/10/07/basic-logic-tips-for-handling-variables
- 2011/10/09/basic-logic-summary
- 2011/10/11/injections-surjections-and-all-that
- 2011/10/13/domains-codomains-ranges-images-preimages-inverse-images
- 2011/10/16/permutations
- 2011/10/23/definitions
- 2011/10/25/alternative-definitions
- 2011/10/30/equivalence-relations
- 2011/10/31/how-might-we-get-to-a-new-model-of-mathematical-publishing
- 2011/11/03/a-more-modest-proposal
- 2011/11/06/group-actions-i
- 2011/11/09/group-actions-ii-the-orbit-stabilizer-theorem
- 2011/11/13/why-isnt-the-fundamental-theorem-of-arithmetic-obvious
- 2011/11/18/proving-the-fundamental-theorem-of-arithmetic
- 2011/11/20/normal-subgroups-and-quotient-groups
- 2011/11/25/group-actions-iii-whats-the-point-of-them
- 2011/11/28/a-short-post-on-countability-and-uncountability
- 2011/12/10/group-actions-iv-intrinsic-actions
- 2011/12/18/farewell-to-a-pen-friend
- 2012/01/17/sopa-my-part-in-its-downfall
- 2012/01/21/elsevier-my-part-in-its-downfall
- 2012/04/28/a-look-at-a-few-tripos-questions-i

*You should treat equivalent properties as alternative definitions.*

ref: 2011/alternative-definitions

high-schools have become a place where false self-esteem is developed, not education

ref: examples-first-ii

- 16-4-2020 How to lose your fear of tensor products
- welcome-to-the-cambridge-mathematical-tripos
- http://www.tricki.org a Wiki-style site with a large store of useful mathematical problem-solving techniques.

2012/06/08/how-should-mathematics-be-taught-to-non-mathematicians

- Connettivi logici. AND OR NOT IF
- Sostituzioni matematiche.
- Gruppo quoziente. Gruppo semplice. Sottogruppo normale.
- Azioni di un gruppo

2cultures.pdf problem_solvers e teorici