Reddit mentions: The best industrial production & management books

Sounds like you are interested in Operations Research as a discipline.

If you are looking for something to give you ideas about what longterm projects and outcomes look like, something like this book here(The Applied Business Analytics Casebook: Applications in Supply Chain Management, Operations Management, and Operations Research) might be good.

If you are looking for something more hands on, then either the Rardin or Nocedal and Wright books might be a good starting point.

For probability, go with Ross every time. Clear and concise, I've found no better book on probability and stochastic processes.

Intro to Probability:
http://www.amazon.com/First-Course-Probability-Sheldon-Ross/dp/013603313X/ref=sr_1_1?ie=UTF8&s=books&qid=1266746119&sr=8-1-spell

Another good introduction, with more advanced modeling topics:
http://www.amazon.com/Introduction-Probability-Models-Ninth-ebook/dp/B000WNFX3O/ref=sr_1_2?ie=UTF8&s=digital-text&qid=1266746119&sr=8-2-spell

Stochastic (random) Processes:
http://www.amazon.com/Stochastic-Processes-Sheldon-M-Ross/dp/0471120626/ref=sr_1_1?ie=UTF8&s=books&qid=1266746101&sr=8-1

What if there are 3 people? Or 4?

Ok, how about a book dedicated to this subject that uses this idea and extends it to voting? https://www.amazon.com/Fair-Division-Cake-Cutting-Dispute-Resolution/dp/0521556449

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And another book: https://www.amazon.com/Cake-Cutting-Algorithms-Fair-You-Can/dp/1568810768

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Optimization Over Time: Dynamic Programming and Stochastic Control (Vol. I & II) Wiley Series in Probability and Statistics - Applied Probability and Statistics Section

https://www.abebooks.co.uk/servlet/BookDetailsPL?bi=22651494592&searchurl=tn%3DOptimization%2BOver%2BTime%252C%2BDynamic%2BProgramming%2Band%2BStochastic%2BControl%2B%2528Wiley%2BSeries%2Bin%2BProbability%2Band%2BStatistics%2B-%2BApplied%2BProbability%2Band%2BStatistics%2BSection%2529%26sortby%3D17%26an%3Dpeter%2Bwhittle&cm_sp=snippet-_-srp1-_-image3

https://www.amazon.com/gp/product/1886529442/ref=ox_sc_act_title_5?smid=ATVPDKIKX0DER&psc=1

https://www.amazon.com/gp/product/0521295149/ref=ox_sc_act_title_10?smid=ATVPDKIKX0DER&psc=1

https://www.amazon.com/gp/product/0471101206/ref=ox_sc_sfl_title_2?ie=UTF8&psc=1&smid=ANKJ1HIJYFVVM

https://www.amazon.com/gp/product/0471104965/ref=ox_sc_sfl_title_3?ie=UTF8&psc=1&smid=A327JZFAPRTZ0D

https://www.amazon.com/gp/product/1886529434

https://www.amazon.com/gp/product/0133796779

https://www.amazon.com/gp/product/1618532332

https://www.amazon.com/gp/product/1259717771
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Cool idea. If you go into business with multiple friends, you can look at the cake-cutting book for other ways to set up the contract.

Some elementary geometry of differentiable curves (check out Gibson's book) would probably be a cool project. This is how differential geometry began, which has applications in physics (the book by Gibson talks about the geometry of trajectories).

Another idea: infinitesimals, the foundations of calculus, and nonstandard calculus (check out Henle or Hrbacek). This also has a historical component, which might make it more interesting. You can substitute nonstandard calculus into most applications of standard calculus, so just use one of those for an application.

A project on a specific function with interesting properties might also be a good idea. For example, the Gamma function, the Lambert W function, or even the Riemann Zeta function to name a few. These pop up in a lot of place in and outside math.

I think the fractional calculus has some applications in quantum physics, but that would probably be hard to talk about.

Indeed, and at least one book on it: https://www.amazon.com/Cake-Cutting-Algorithms-Fair-You-Can/dp/1568810768

Genetic algorithms (GAs), the most popular type of evolutionary algorithm, have attracted a lot of attention in the past. They're generally used to attack NP-hard problems, which basically means that the problems don't have a fast way of directly solving them and you'll have to settle for an approximation for serious problems. When it comes to solving these types of problems, you can imagine a large space that needs searching in some manner, where the dimensionality is usually very high. GAs work by combining information from candidate solutions in the space. Combining solutions can be slow and there's usually no reason that combining solutions the way GAs do should be very useful. Even worse, depending on the type of problem you're attacking and the way you encode solutions, the new candidate solution might not even be viable in the space.

I took a course in optimization where the book pretty much flat out said that GAs aren't worth it. I've spent some time working with these things and I found that, for my problems, implementing a local search component made it run faster, pretty much in proportion to how much I integrated the local search. I think GAs are really cool conceptually and people should know how they work, but I would not reach for one to solve a real problem.

From the GA Wikipedia page: "The question of which, if any, problems are suited to genetic algorithms (in the sense that such algorithms are better than others) is open and controversial."