Here's what I'd recommend.

GETTING STARTED WITH DATA SCIENCE

If you're interested in learning data science I'd suggest the following:
 

Tools

1. I’d recommend learning R before Python (although Python is an exceptional tool). Here are a few reasons.
   
   1. Many of the hot tech companies in SF, the Valley, and NYC like Google, Apple, FB, LinkedIn, and Twitter are using R for much of their data science (not all of it, but a lot).
      
   2. R is the most common programming language among data scientists. O’Reilly Media just released their 2014 Data Science Salary Survey. I’ll caveat though, that Python came in at a close second. Which leads me to the third reason:
      
   3. R has 2 packages that dramatically streamline the DS workflow:
      
      • dplyr for data manipulation
        
      • ggplot2 for data visualization
        
        Learning these has several benefits: they streamline your workflow. They speed up your learning process, since they are very easy to use. And perhaps most importantly, they really teach you how to think about analyzing data. GGplot2 has a deep underlying structure to the syntax, based on the Grammar of Graphics theoretical framework. I won’t go into that too much, but suffice it to say, when you learn the ggplot2 syntax, you’re actually learning how to think about data visualization in a very deep way. You’ll eventually understand how to create complex visualizations without much effort.
         
        
        Skill Areas
        My recommendations are:
        
        
2. Learn basic data visualizations first. Start with the essential plots:
   
   • the scatter plot
     
   • the bar chart
     
   • the line chart
     (But, again I recommend learning these in R’s ggplot2.) The reason I recommend these is
     
     1. The are, hands down, the most common plots. For entry level jobs, you’ll use these every day.
        
     2. They are “foundational” in the sense that when you learn about the underlying structure of these plots, it begins to open up the world of complex data visualizations.
        As with any discipline, you need to learn the foundations first; this will dramatically speed your progress in the intermediate to advanced stages.
        
     3. You’ll need these plots as “data exploration” tools. Whether you’re finding insights for your business partners or investigating the results of a sophisticated ML algorithm, you’ll likely be exploring your data visually.
        
     4. These plots are your best “data communication” tools. As noted elsewhere in this thread, C-level execs need you to translate your data-driven insights into simple language that can be understood in a 1-hour meeting. Communicating visually with the basic plots will be your best method for communicating to a non-technical audience. Communicating to non-technical audiences is a critical (and rare) auxiliary skill, so if you can learn to do this you will be very highly valued by management.
        I usually suggest learning these with dummy data (for simplicity) but if you have a simple .csv file, that should work to.
        
3. Learn data management second (AKA, data wrangling, data munging)
   After you learn data visualization, I suggest that you “back into” data management. For this, you should find a dataset and learn to reshape it.
   The core data management skills:
   
   • subsetting (filtering out rows)
     
   • selecting columns
     
   • sorting
     
   • adding variables
     
   • aggregating
     
   • joining
     You can start learning these here. Again, I recommend learning these in R’s dplyr because dplyr makes these tasks very straight forward. It also teaches you how to think about data wrangling in terms of workflow: the “chaining operator” in dplyr helps you wire these commands together in a way that really matches the analytics workflow. dplyr makes it seamless.
     
4. Learn machine learning last.
   ML is sort of like the “data science 301” course vs. the 102 and 103 levels of the data-vis and data manipulation stuff I outlined above.
   Here, I’ll just give book recos:
   
   • An Introduction to Statistical Learning.
     This is a highly regarded introduction
     
   • Machine Learning with R
     
   • I’ve also heard that there is some foundational ML information in R in Action, though I haven’t read it myself.
     
     After you get these foundations, then you can move on to specialize in a particular area.
      
     

     OTHER RESOURCES:
     

     Data Visualization
     

5. Nathan Yao of Flowing Data is great. His blog shows excellent data visualization examples. Also, I highly recommend his books. In particular, Data Points. Data Points will help you learn how to think about visualization.
   
6. The book ggplot2 by Hadley Wickham. This is a great resource (though a little outdated, as Hadley has updated the ggplot package).
   
7. I also really like Randal Olson’s work (AKA, /u/rhiever). He creates some great data visualizations that can serve as inspiration as you start learning.
    
   

   TL;DR
   

   I'd recommend learning R for data science before Python. Learn data visualization first (with R's ggplot2), using simple data or dummy data. Then find a more complicated dataset. Learn data manipulation second (with R's dplyr), and practice data manipulation on your more complex data. Learn machine learning last.

> Mathematical Logic

It's not exactly Math Logic, just a bunch of techniques mathematicians use. Math Logic is an actual area of study. Similarly, actual Set Theory and Proof Theory are different from the small set of techniques that most mathematicians use.

Also, looks like you have chosen mostly old, but very popular books. While studying out of these books, keep looking for other books. Just because the book was once popular at a school, doesn't mean it is appropriate for your situation. Every year there are new (and quite frankly) pedagogically better books published. Look through them.

Here's how you find newer books. Go to Amazon. In the search field, choose "Books" and enter whatever term that interests you. Say, "mathematical proofs". Amazon will come up with a bunch of books. First, sort by relevance. That will give you an idea of what's currently popular. Check every single one of them. You'll find hidden jewels no one talks about. Then sort by publication date. That way you'll find newer books - some that haven't even been published yet. If you change the search term even slightly Amazon will come up with completely different batch of books. Also, search for books on Springer, Cambridge Press, MIT Press, MAA and the like. They usually house really cool new titles. Here are a couple of upcoming titles that might be of interest to you: An Illustrative Introduction to Modern Analysis by Katzourakis/Varvarouka, Understanding Topology by Shaun Ault. I bet these books will be far more pedagogically sound as compared to the dry-ass, boring compendium of facts like the books by Rudin.

If you want to learn how to do routine proofs, there are about one million titles out there. Also, note books titled Discrete Math are the best for learning how to do proofs. You get to learn techniques that are not covered in, say, How to Prove It by Velleman. My favorites are the books by Susanna Epp, Edward Scheinerman and Ralph Grimaldi. Also, note a lot of intro to proofs books cover much more than the bare minimum of How to Prove It by Velleman. For example, Math Proofs by Chartrand et al has sections about doing Analysis, Group Theory, Topology, Number Theory proofs. A lot of proof books do not cover proofs from Analysis, so lately a glut of new books that cover that area hit the market. For example, Intro to Proof Through Real Analysis by Madden/Aubrey, Analysis Lifesaver by Grinberg(Some of the reviewers are complaining that this book doesn't have enough material which is ridiculous because this book tackles some ugly topological stuff like compactness in the most general way head-on as opposed to most into Real Analysis books that simply shy away from it), Writing Proofs in Analysis by Kane, How to Think About Analysis by Alcock etc.

Here is a list of extremely gentle titles: Discovering Group Theory by Barnard/Neil, A Friendly Introduction to Group Theory by Nash, Abstract Algebra: A Student-Friendly Approach by the Dos Reis, Elementary Number Theory by Koshy, Undergraduate Topology: A Working Textbook by McClusckey/McMaster, Linear Algebra: Step by Step by Singh (This one is every bit as good as Axler, just a bit less pretentious, contains more examples and much more accessible), Analysis: With an Introduction to Proof by Lay, Vector Calculus, Linear Algebra, and Differential Forms by Hubbard & Hubbard, etc

This only scratches the surface of what's out there. For example, there are books dedicated to doing proofs in Computer Science(for example, Fundamental Proof Methods in Computer Science by Arkoudas/Musser, Practical Analysis of Algorithms by Vrajitorou/Knight, Probability and Computing by Mizenmacher/Upfal), Category Theory etc. The point is to keep looking. There's always something better just around the corner. You don't have to confine yourself to books someone(some people) declared the "it" book at some point in time.

Last, but not least, if you are poor, peruse Libgen.

If you are really interested in theory, start with some material in automata theory. My favorite textbook as an undergrad was Automata & Computability by Kozen, but there are many others (lots of people like Sipser's book, but it's pretty terse). This material is a more classical side of CS, and many view it as outdated. But the theory is elegant & beautiful, and the concepts do underlie many other parts of CS. More importantly, you will start to think of computation as a completely abstract process, divorced from any particular technology.

Automata theory provides a good foundation for compiler theory, and I think it's a great exercise to write a compiler during an undergrad CS degree.

You might also want to look into cryptography (warning: biased crypto opinion to follow). I wouldn't say that crypto is essential in a CS curriculum, but it sure is fun, and thinking formally about security is a good habit for any engineer. The field runs the gamut, from the very pragmatic influence from the systems community, to completely theoretical and abstract influence from the complexity community, and the pure math foundations from abstract algebra. If you dig around a bit, you can surely find a mixture of number theory / abstract algebra, computation, theory, and practice that suits you. Katz/Lindell is the most theoretical undergrad crypto text you're likely to encounter. Stinson has a nice book that is a safer mix of theory & practice.

A graph theory project! I just started today (it was assigned on Friday and this is when I selected my topic). I’m on spring break but next month I have to present a 15-20 minute lecture on graph automorphisms. I don’t necessarily have to, but I want to try and tie it in with some group theory since there is a mix of undergrads who the majority of them have seen some algebra before and probably bored PhD students/algebraists in my class, but I’m not sure where to start. Like, what would the binary operation be, composition of functions? What about the identity and inverse elements, what would those look like? In general, what would the elements of this group look like? What would the group isomorphism be? That means it’s a homomorphism with a bijective function. What would the homomorphism and bijective function look like? These are the questions I’m trying to get answers to.

Last semester I took a first course in Abstract Algebra and I’m currently taking a follow up course in Linear Algebra (I have the same professor for both algebra classes and my graph theory class). I’m curious if I can somehow also bring up some matrix representation theory stuff as that’s what we’re going over in my linear algebra class right now.

This is the textbook I’m using for my graph theory class: Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/1846289696?ref=yo_pop_ma_swf

Here are the other graph theory books I got from my library and am using as references: Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/3662536218?ref=yo_pop_ma_swf

Modern Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/0387984887?ref=yo_pop_ma_swf

And for funsies, here is my linear algebra text: Linear Algebra, 4th Edition https://www.amazon.com/dp/0130084514?ref=yo_pop_ma_swf

But that’s what I’m working on! :)

And I certainly wouldn’t mind some pointers or ideas or things to investigate for this project! Like I said, I just started today (about 45 minutes ago) and am just trying to get some basic questions answered. From my preliminary investigating in my textbook, it seems a good example to work with in regards to a graph automorphism would be the Peterson Graph.

Just a few ideas...

• Nerdy stuff from ThinkGeek.
  
• A Raspberry Pi kit, if you think he'd be into tinkering with hardware.
  
• It's probably going to be more than $70, but a nice mechanical keyboard is a great gift. Das Keyboard, Code, and Logitech G710+ are safe choices.
  
• Book-wise, consider Code. It's a classic for every programmer to read.

Three books I have been using:

The Definitive Guide to How Computers Do Math

Web page here: http://www.diycalculator.com/

Assembly Language Step-by-Step: Programming with Linux

Hacking: The Art of Exploitation, 2nd Edition

The first uses a virtual machine running on Windows, with 5 registers, 65K of virtual memory, a debugger, and will give you a good basic understanding of what is going on. The second book uses Intel X86 on Linux, and gives a solid foundation of the most used instructions. The third book is just good.

Other favorites of mine include "The Art of Debugging" by Norm Matloff (google for his excellent web page) and "Professional Assembly Language" by Richard Blum.

Have fun!

As an AI professor...thank you.

We have made fantastic progress over the last 40 years on highly domain-specific tasks, including some that seemed out of reach a few years ago (looking at you, Go). However, our general reasoning progress has hardly put us ahead of this interesting collection of research published in 1968. (A couple of the chapters there talk about how much better computers will do in a few years when they have more than 64KB of memory and run faster than a few MHz. Sigh.)

Nice to see the actual state of the art highlighted for once.

Implementing SSL/TLS

https://www.amazon.com/Implementing-SSL-TLS-Joshua-Davies/dp/0470920416/ref=sr_1_4?keywords=openssl&qid=1550253200&s=gateway&sr=8-4

practical guide to implementing SSL and TLS. All examples are written in C with the implementation of DES, AES, RC4, Large Integer Arithmetic, RSA, Deffie-Hellman, HMAC, DSA, Elliptic Curve, X.509.

​

For me, the best theoretical books on cryptography, but without deep immersion in mathematics:

Understanding Cryptography: A Textbook for Students and Practitioners

https://www.amazon.com/Understanding-Cryptography-Textbook-Students-Practitioners/dp/3642041000/ref=sr\_1\_1?crid=3700J8SGJK4QP&keywords=understanding+cryptography&qid=1550253725&s=gateway&sprefix=Undes%2Caps%2C295&sr=8-1

and it goes better with video lectures https://www.youtube.com/channel/UC1usFRN4LCMcfIV7UjHNuQg

​

A good book on cryptanalysis for symmetric algorithms:

The Block Cipher Companion (Information Security and Cryptography)

https://www.amazon.com/Cipher-Companion-Information-Security-Cryptography/dp/3642173411/ref=sr_1_fkmrnull_1?crid=NNR5L5I1VYK2&keywords=block+cipher+companion&qid=1550253926&s=gateway&sprefix=The+Block+cipher+%2Caps%2C340&sr=8-1-fkmrnull

​

good exercise: http://cryptopals.com/

​

For the basics of mathematics I usually suggest "Mathematics for Computer Graphics" by John Vince.

https://www.amazon.com/dp/1447173341

On physics, there are a number of specialised books. Nevertheless, if with "physics" you mean "movement", the third chapter of "Artificial Intelligence for Games" by Ian Millington is for you (beware, source code is provided in C++, not C#).

https://www.amazon.com/dp/0123747317

About shaders, there are a number of sources out there. From a didactical standpoint I like the following two blogs:

https://www.alanzucconi.com/

http://catlikecoding.com/

And another interesting source is also http://www.shaderslab.com/shaders.html

If you prefer a book, a good primer can be "2D Shader Development: Foundations" by Francisco Tufro. Not the absolute best, but may give you a nice jumpstart in a limited number of pages

https://www.amazon.com/dp/B07BGYF7F8 (also available from the author's website).

Happy hacking.

In the right environment this can be resolved by the compiler, but presently all of the "behind the scenes" compiling is a black box that actually varies in what results you get! If you are really interested you can check out this book that proposes a better solution: www.amazon.com/The-End-Error-Computing-Computational/dp/1482239868

Bioethics in bioinformatics, especially in a clinical context, is a fairly active area. It can be viewed as a subfield of computing ethics or the ethics of information.. For e.g. see: Ethics in Computing and Information Ethics and Philosophy of Information. As bio-augmentation technologies proliferate, issues surrounding the personal, ethical, legal, and socio-philosophical implications of bioinformation - its generation, use, storage, handling, persistence , ownership - will get quite complex. So, your thoughts may be worth having!

The NIH Bioethics department may be good place to investigate. If you are an experienced professional, just go on and write a paper and ship it off to a journal. If you don't know where to start, put something on paper and find a collaborator that you can work with - they may be found in hospitals, law schools and/or departments of philosophy, social science .... endless options.

NIH Bioethics

Fellowships

Excellent reference texts that will give you a good idea of what you are getting yourself into:

• Discreet Structures, Logic, and Computability - Hein
  
• Introduction to Algorithms - Cormen, Leiserson, Rivest and Stein
  
• Artifical Intelligence: A modern Approach - Norvig
  
  edit - borken link

Ingo Wegener: Theoretische Informatik: ― eine algorithmenorientierte Einführung (German).

Incredibly dense work. Forces you to think through the topics presented. Definitely makes the lessons stick.

Great book for anyone interested in the theory of CS (Turing machines, Church-Turing thesis, P/NP, Chomsky Hierarchy, ...).

Check out "The Definitive Guide to How Computers Do Math : Featuring the Virtual DIY Calculator." It's not a textbook, but it is a pretty good guide to computer architecture with a lot of hands-on labs to work through.

https://www.amazon.com/Definitive-Guide-How-Computers-Math/dp/0471732788

Always liked Introduction to Automata Theory, Languages, and Computation by Hopcroft and Ullman as an intro text. Undergraduate-level but good treatment of TCS.

If that's too basic, I recommend Theory of Computation by Kozen. It's roughly 1st-year graduate level, intended for those already with some background.

If that's too basic, for a research-level survey of TCS, take a look at Wigderson's Mathematics and Computation.

I'd recommend these two for discrete mathematics, I used them during my time in university and they were pretty helpful

I'm just getting started myself. I have ordered this book: http://www.amazon.com/Course-Applied-Mathematics-Computing-Science/dp/0198538030/ref=sr_1_1?s=books&ie=UTF8&qid=1346174013&sr=1-1

I hope it's good :)

Some schools don't cover much in the way of discrete math, formal languages, automata, or proofs... at least not very rigorously. My opinion here is colored by my own experience (and subsequent disappointment, but thats another story), and I'm sure most schools sort of exist on a spectrum. YMMV.

Some books that come to mind (might not be to surprising if you spend a lot of time on CS forums):

[Introduction to the Theory of Computation](
https://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser-ebook/dp/B00B63LSA6)

CLRS Introduction to Algorithms

SICP

I think it's interesting to look at the history of computer science-- read about Bertrand Russel, David Hilbert, the Vienna Circle, Alonzo Church and his students (Alan Turing was one). Computer Science as an academic discipline was kind of born from the questions mathematicians and philosophers were trying to ask in the early 20th century. It's just as much about language as it is about mathematics. I could probably write a wall of text on the topic, but I'll just leave it at that. :)

Here are all the local Amazon links I could find:


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I’m a fan of this one:

Algebra for Cryptologists (Springer Undergraduate Texts in Mathematics and Technology) https://www.amazon.com/dp/3319303953/ref=cm_sw_r_cp_api_Y86XAbKGQE9X2

It talks about the abstract algebra material at an easy to approach undergraduate level and shows how the abstract algebra topics can be applied. It’s part computational and part theoretical which I think is good going at it for the first time.

I'm a Linguistic BS student, but I've taken many CS classes as a minor and greatly enjoyed them. There's a lot of programming that you don't learn easily from just doing.

The book from that class was this one. Note that it's a CS book, not a programming book, and so a lot of it is based on a knowledge of discrete structures and mathematics (at least a good deal of algebra). Before I took that class I had to take a class that used this book, which is based more-so on logic and discrete mathematics than anything else.

You won't learn to program from those books. What you will learn is the fundamentals behind the data structures and algorithms that every major language is based on. When I learn a new language, I find myself understanding the various data structures very quickly because I have theoretical background. My friend who has a more IT-oriented background from a different college usually has to learn the details of new languages by analogy, and it seems to take him some time.

How about books:

"Machine Learning with R" [1] or "Building Machine Learning Systems with Python" [2]

I have both of those, they're pretty good for beginning IMHO. They provide datasets and code and show analysis after the fact.


[1] -- http://www.amazon.com/Machine-Learning-R-Brett-Lantz-ebook/dp/B00G9581JM/ref=sr_1_1?s=books&ie=UTF8&qid=1407184441&sr=1-1&keywords=machine+learning+with+r

[2] -- http://www.amazon.com/Building-Machine-Learning-Systems-Python-ebook/dp/B00E7NC9D2/ref=sr_1_1?s=books&ie=UTF8&qid=1407184471&sr=1-1&keywords=python+machine+learning

Update

Looks like there are some further links

• Youtube Talk Mark Horowitz
  
• IEEE: 1.1 Computing's energy problem (and what we can do about it)
  
• Amazon UK Book: The End of Error, Unum computing - John L Gustafson (the USA version is linked in the article. I Have no affiliation but it's apparently where the figures came from)
  
  Looks like I won't get cheap, or fast answers to my questions... So life continues and this will be added to the pile of things I'm vaguely interested in but probably cannot apply.

Automata & Computability by Dexter Kozen is not only my favorite CS theory book, but one of my favorite books in any category.

There are quite a few different types of cryptographic algorithms, some requiring more mathematics to get started than others. But it seems like you might be interested in block ciphers or stream ciphers.

/u/remyroy recommended rotation ciphers, which are probably the simplest and easiest to break.

The NSA has recently produced simple, but important, ciphers: Simon and Speck; release document and Bruce Schneier's comment. It will be difficult to break these ciphers, but at least this might lead you on a path to try to understand what it means to break a cipher.

If you want more information on block ciphers and how to break them, there's The Block Cipher Companion and I found this tutorial on differential and linear cryptanalysis which might provide a gentle introduction, but I haven't read it.

Anyway, have fun.

Kozen's book is basically preparation for a ToC prelim. Seems good to me.

Another good one, though more specific: http://www.amazon.com/Definitive-Guide-How-Computers-Math/dp/0471732788/ref=sr_1_1?s=books&ie=UTF8&qid=1411695108&sr=1-1

This book might help you: http://www.amazon.com/gp/aw/d/B008PGKDOO?vs=1

Yeah, I've heard the same things about Rosen, but I wanted to mention it since the video lectures use Rosen.

The book that the discrete class I'm taking next semester will be using is "Essentials of Discrete Mathematics" by David J. Hunter. From what I have seen, looking through the text, it covers many of the basic materials in a Discrete class. This should be an okay book to use if you find that Rosen isn't to your liking.

If you want a more mathematical basis you can get the following:

Introduction to Mathematical Cryptography

Algebra for Cryptologists

Check out Dexter Kozen's book Automata and Computability, it's a very well formatted book in that it consists of a series of lectures as opposed to a typical textbook with chapters and such. There are practice problems for each lecture too.

Kozen is very highly regarded in the field of theoretical computer science.

https://www.amazon.com/gp/aw/d/0387949070/ref=pd_aw_sim_sbs_14_2/166-2338586-0066212?ie=UTF8&psc=1&refRID=WTB3YAPD3T8RPYC2FBTR