31–40 of 59 posts
Proofs from the Book looks superb but does anyone know of another introduction to proofs or compendium of simple proofs suitable for young mathematicians?
The main downside is that there isn't an official solution manual, so checking your work takes a little more work. But one of the main upsides is that there isn't an official solution manual, so you actually have to work through the problems. :)
Many of the list are pop-maths rather than fundamental texts. I do see many in software field recommend Chrystal:Algebra an Elementary Textbook. I also find Don Knuth, 'Concrete Mathematics' a interesting book for software people.
Any good recommendations on books that are more than pop-fluff but lighter than an academic text?
Many of the list are pop-maths rather than fundamental texts. I do see many in software field recommend Chrystal:Algebra an Elementary Textbook. I also find Don Knuth, 'Concrete Mathematics' a interesting book for software people.
I came to a realization years ago that when it comes to math/science/computers, if I just read about it, I’m not really learning anything. I don’t learn unless I’m participating. Math books without _lots_ of exercises probably don’t really impart that much, although they can be a fun distraction if you need something to read on an airplane.
Earlier quoted context omitted.
I came to a realization years ago that when it comes to math/science/computers, if I just read about it, I’m not really learning anything. I don’t learn unless I’m participating. Math books without _lots_ of exercises probably don’t really impart that much, although they can be a fun distraction if you need something to read on an airplane.
Depending on your level of math ability you can often learn a lot by reading textbooks and proofs very carefully and closely (my opinion)
But everyone I know who is able to teach themselves math without lectures or a professor still does the exercises in the textbook. Math isn't a spectator sport, it's really important to do active learning.
Many of the list are pop-maths rather than fundamental texts. I do see many in software field recommend Chrystal:Algebra an Elementary Textbook. I also find Don Knuth, 'Concrete Mathematics' a interesting book for software people.
Any good recommendations on books that are more than pop-fluff but lighter than an academic text?
Earlier quoted context omitted.
Any good recommendations on books that are more than pop-fluff but lighter than an academic text?
I really liked Introduction to Graph Theory by Trudeau. No upper level math required, but it got rigorous and fun at times. Mostly spatial reasoning. David Foster Wallace wrote Everything and More which included a lot of math history, while driving into transfinite numbers and set theory. Kindle typesetting is generally terrible for math, but was completely readable in this case. The forward by Neal Stephenson really…
This is far and away my favorite math book. The way DFW can seamlessly transition from discussing a serious mathematical concept, to the nature of insanity, to the philosophy of abstraction all within a few pages is astounding. He somehow manages to do it while maintaining a conversational, two-folks-at-a-bar tone, teaching me dozens of new word, and being insightful/funny. Like an English professor sneaked into the math dept.
I didn't know it was available on Kindle. Guess I'm buying it again...
Earlier quoted context omitted.
I came to a realization years ago that when it comes to math/science/computers, if I just read about it, I’m not really learning anything. I don’t learn unless I’m participating. Math books without _lots_ of exercises probably don’t really impart that much, although they can be a fun distraction if you need something to read on an airplane.
Depending on your level of math ability you can often learn a lot by reading textbooks and proofs very carefully and closely (my opinion)
Before buying a copy of Prime Obsession , please learn more about the author: https://en.wikipedia.org/wiki/John_Derbyshire I bought and read his book some time ago, and now I regret supporting him with my purchase.
> There have of course been some blots on the record, but I don't see how it can be denied that net-net, white Europeans have made a better job of running fair and stable societies than has any other group. If colonialism, WW2 and USSR are 'blots' he might have to reexamine his definition of 'blot'. White supremacists hold themselves up as people willing to speak difficult truths. But their logic tends to be pretty q…
Many of the list are pop-maths rather than fundamental texts. I do see many in software field recommend Chrystal:Algebra an Elementary Textbook. I also find Don Knuth, 'Concrete Mathematics' a interesting book for software people.
Any good recommendations on books that are more than pop-fluff but lighter than an academic text?
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Aleksandrov et al - Mathematics: Its content, Methods, ad Meaning. Overview of undergrad curriculum by a number of prominent russian mathematicians.
Levi - The mathematical Mechanic. Uses various physical intuitions and scenarios to solve mathematical problems.
Pask - Magnificent Principia. Tour of newtons principia that includes both newtons geometric language and modern vector calculus version.
Stillwell - Elements of Mathematics. Discusses some important classical problems in the history of mathematics taken from 8 subjects: arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, logic. Wow!
Yandell - The Honors Class: Hilbert's problems and their solvers. Lots of mini biographies with some information describing each of Hilbert's famous problems.
Lawvere & Schanuel- Conceptual Mathematics. Some basic notions of category theory, geared towards teaching you Lawvere's clarification and generalization of the incompleteness theorems.
Cormen - Algorithms Unlocked. Pop Science version of some of the textbook.
Nahin - Inside interesting Integrals. Lots of fun integrations!
Nahin - He also wrote some books about euler and imaginary numbers which ive partially read, they seemed good.
Pierce - An introduction to information theory; symbols signals and noise. sounds and looks like a dover textbook but is a non-fake pop science book.
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Boyer - The History of Calculus and its Conceptual Development. A bit old, and spends too much time on formalism in the 18th and 19th century, there might be something better out now.
Weyl - Philosophy of Mathematics and Natural Science.
Reichenbach - The philosophy of Space and time.
Klein - Elementary mathematics from the advanced viewpoint. these were written at the beginning of the 20th century so are slightly outdated, but kline was extremely forward-looking in his point of view.
Courant & Robbins - What is Mathemaics. Another classic.
Hilbert & Cohn-Vossen - Geometry and the Imagination. The gold standard of popular mathematics writing. A beautiful book.