25 Matching Annotations
  1. Jan 2023
    1. Woit does provide problems, but they are all at the back of the book. It would have been better to see them between chapters. That provides a natural break in the material and gives the student a quick check on his understanding.

      Homework problems are pedagogical devices and many (most) authors place them in the text near where they would be profitably be done. They also provide a useful break in the text to prompt more novice students to actually perform them at the end of a section.

      More advanced students, however, should have caught on eventually at the need to work out examples for themselves which are presented in a textbook, but they should also be seeking out additional problems where ever they appear in the text, not to mention seeing out any outside additional problems, making up their own, and exploring any additional questions these pose.

      In mathematics textbooks this working of problems, expanding on them and seeking out new ones is often a large part of what is lurking behind the sometimes nebulous sounding idea of "mathematical sophistication". The rest of that equation typically includes experience with the various methods and means of proofs and some basic background in logic.

    2. Woit does not, for the most part, follow the death march of proposition, lemma, proof. He writes in the style of a theoretical physicist.

      "death march of proposition, lemma, proof"

      This is a bit harsh n'cest pas?

  2. Dec 2022
    1. My freely downloadable Beginning Mathematical Logic is a Study Guide, suggesting introductory readings beginning at sub-Masters level. Take a look at the main introductory suggestions on First-Order Logic, Computability, Set Theory as useful preparation. Tackling mid-level books will help develop your appreciation of mathematical approaches to logic.

      This is a reference to a great book "Beginning Mathematical Logic: A Study Guide [18 Feb 2022]" by Peter Smith on "Teach Yourself Logic A Study Guide (and other Book Notes)". The document itself is called "LogicStudyGuide.pdf".

      It focuses on mathematical logic and can be a gateway into understanding Gödel's incompleteness theorems.

      I found this some time ago when looking for a way to grasp the difference between first-order and second-order logics. I recall enjoying his style of writing and his commentary on the books he refers to. Both recollections still remain true after rereading some of it.

      It both serves as an intro to and recommended reading list for the following: - classical logics - first- & second-order - modal logics - model theory<br /> - non-classical logics - intuitionistic - relevant - free - plural - arithmetic, computability, and incompleteness - set theory (naïve and less naïve) - proof theory - algebras for logic - Boolean - Heyting/pseudo-Boolean - higher-order logics - type theory - homotopy type theory

  3. Nov 2022
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  9. Mar 2021
    1. To the consternation of some users, 3.x employed Unicode variable names such as λ, φ, τ and π for a concise representation of mathematical operations. A downside of this approach was that a SyntaxError would occur if you loaded the non-minified D3 using ISO-8859-1 instead of UTF-8. 3.x also used Unicode string literals, such as the SI-prefix µ for 1e-6. 4.0 uses only ASCII variable names and ASCII string literals (see rollup-plugin-ascii), avoiding encoding problems.
  10. Feb 2021
  11. Jul 2020
    1. Most of Algol's "special" characters (⊂, ≡, ␣, ×, ÷, ≤, ≥, ≠, ¬, ⊃, ≡, ∨, ∧, →, ↓, ↑, ⌊, ⌈, ⎩, ⎧, ⊥, ⏨, ¢, ○ and □) can be found on the IBM 2741 keyboard with the APL "golf-ball" print head inserted; these became available in the mid-1960s while ALGOL 68 was being drafted. These characters are also part of the Unicode standard and most of them are available in several popular fonts.
  12. Jun 2020
    1. Kucharski, A. J., Klepac, P., Conlan, A. J. K., Kissler, S. M., Tang, M. L., Fry, H., Gog, J. R., Edmunds, W. J., Emery, J. C., Medley, G., Munday, J. D., Russell, T. W., Leclerc, Q. J., Diamond, C., Procter, S. R., Gimma, A., Sun, F. Y., Gibbs, H. P., Rosello, A., … Simons, D. (2020). Effectiveness of isolation, testing, contact tracing, and physical distancing on reducing transmission of SARS-CoV-2 in different settings: A mathematical modelling study. The Lancet Infectious Diseases, 0(0). https://doi.org/10.1016/S1473-3099(20)30457-6

  13. Jan 2014
    1. Once a searchable atlas has been constructed there are fundamentally two approaches that can be used to analyze the data: one visual, the other mathematical.