Reddit mentions of The Language of Mathematics: Making the Invisible Visible

Hi,

I'm a TA in my school's CS theory course (a mixture of discrete math, and the automata, languages and complexity topics most CS theory courses cover).

As others have said, "theory" is pretty broad, so there are an awful lot of resources you could look at. As far as textbooks go, we use two - Sipser's Introduction to the Theory of Computation (which others have recommended), and the freely available textbook Mathematics for Computer Science, by Lehman, Leighton and Meyer - which concentrates more on the "discrete math" side of things. Both seem fine to me. Another discrete-math–focused set of notes is by James Aspnes (PDF here) and seems to have some good introductions to these topics.

If you feel that you're "terrible at studying for these types of courses", it might be worth stepping back a bit and trying to find some sort of an intro to university-level math that resonates for you. A few books I've recommended to people who said they were "terrible at uni-level math", but now find it quite interesting, are:

• Keith Devlin, The Language of Mathematics: Making the Invisible Visible
  
• Ian Stewart, Concepts of Modern Mathematics
  
• Martin Liebeck, A Concise Introduction to Pure Mathematics (rather terser than the previous two, but still a lot gentler than some uni-level texts)
  
  These aren't specific to computer science, but might be of help. Good luck!
  
  
  

Thanks for the reply! I'm doing my AS-levels in Maths, Further, Physics, and computing. Also, very interested to hear your recommendation for Physics. For math im looking at these books:

• Mathematician's Delight
  
• Journey Through Genius
  
• Mathematics and the Physical World
  
• The Mathematical Experience
  
• Language of Mathematics
  
• How to Prove It: A Structured Approach
  
  Tell me what you think

I fall firmly on the discovered side of the debate although I have had this discussion many times before. I believe math exists independently of humanity and that math is simply a tool used to describe patterns in a logical and rigorous way, but that those patterns have always and will always be in the universe and did not need us in order to exist.The driving force in the history of mathematics has not been practical invention by someone determined to solve an existing problem but by investigation of someone into a pattern that they saw or suspected that they saw. Math ends up being useful to people who want to solve a real world problem, but very little math gets created to solve a real world problem. Mostly because the real world problem didn't exist before the math, or that some very clever person saw the math and realized it could be adapted to solve a longstanding problem.

A great book for non mathematicians covering the history of how math came to be what it is today, and all of the impressive fundamental changes that had to occur in the way we though about math would be The Language of Mathematics by Kevin Devlin, a professor of mathematics at Stanford University. My favorite bit from the book is that things that we think are very simple in fact took thousands of years for humans to abstract and notice the patterns. Egyptians for example basically knew the formula for the volume of a pyramid. However we have not a shred of a formula from that period. Instead they treated each set of dimensions a pyramid could have to be a separate problem and therefore failed to notice the formula that was right in front of their faces. It took the greeks (and a good deal of time) for someone to notice the pattern between all pyramid formulas and abstract it into a general solution to the pyramid volume problem.

I'll throw out some of my favorite books from my book shelf when it comes to Computer Science, User Experience, and Mathematics - all will be essential as you begin your journey into app development:

Universal Principles of Design

Dieter Rams: As Little Design as Possible

Rework by 37signals

Clean Code

The Art of Programming

The Mythical Man-Month

The Pragmatic Programmer

Design Patterns - "Gang of Four"

Programming Language Pragmatics

Compilers - "The Dragon Book"

The Language of Mathematics

A Mathematician's Lament

The Joy of x

Mathematics: Its Content, Methods, and Meaning

Introduction to Algorithms (MIT)

If time isn't a factor, and you're not needing to steamroll into this to make money, then I'd highly encourage you to start by using a lower-level programming language like C first - or, start from the database side of things and begin learning SQL and playing around with database development.

I feel like truly understanding data structures from the lowest level is one of the most important things you can do as a budding developer.