If you're looking to learn Python then Practical Programming: An Introduction to Computer Science Using Python 3 is what I recommend. How to Think Like a Computer Scientist: Learning with Python is also very good.

Now in terms of the question that you ask in the title - this is what I recommend:

Job Interview Prep

1. Cracking the Coding Interview: 189 Programming Questions and Solutions
   
2. Programming Interviews Exposed: Coding Your Way Through the Interview
   
3. Introduction to Algorithms
   
4. The Algorithm Design Manual
   
5. Effective Java
   
6. Concurrent Programming in Java™: Design Principles and Pattern
   
7. Modern Operating Systems
   
8. Programming Pearls
   
9. Discrete Mathematics for Computer Scientists
   
   

   Junior Software Engineer Reading List
   

   
   

   Read This First
   

   
   

10. Pragmatic Thinking and Learning: Refactor Your Wetware
    
    

    Fundementals
    

    
    

11. Code Complete: A Practical Handbook of Software Construction
    
12. Software Estimation: Demystifying the Black Art
    
13. Software Engineering: A Practitioner's Approach
    
14. Refactoring: Improving the Design of Existing Code
    
15. Coder to Developer: Tools and Strategies for Delivering Your Software
    
16. Perfect Software: And Other Illusions about Testing
    
17. Getting Real: The Smarter, Faster, Easier Way to Build a Successful Web Application
    
    

    Understanding Professional Software Environments
    

    
    

18. Agile Software Development: The Cooperative Game
    
19. Software Project Survival Guide
    
20. The Best Software Writing I: Selected and Introduced by Joel Spolsky
    
21. Debugging the Development Process: Practical Strategies for Staying Focused, Hitting Ship Dates, and Building Solid Teams
    
22. Rapid Development: Taming Wild Software Schedules
    
23. Peopleware: Productive Projects and Teams
    
    

    Mentality
    

    
    

24. Slack: Getting Past Burnout, Busywork, and the Myth of Total Efficiency
    
25. Against Method
    
26. The Passionate Programmer: Creating a Remarkable Career in Software Development
    
    

    History
    

    
    

27. The Mythical Man-Month: Essays on Software Engineering
    
28. Computing Calamities: Lessons Learned from Products, Projects, and Companies That Failed
    
29. The Deadline: A Novel About Project Management
    
    

    Mid Level Software Engineer Reading List
    

    
    

    Read This First
    

    
    

30. Personal Development for Smart People: The Conscious Pursuit of Personal Growth
    
    

    Fundementals
    

    
    

31. The Clean Coder: A Code of Conduct for Professional Programmers
    
32. Clean Code: A Handbook of Agile Software Craftsmanship
    
33. Solid Code
    
34. Code Craft: The Practice of Writing Excellent Code
    
35. Software Craftsmanship: The New Imperative
    
36. Writing Solid Code
    
    

    Software Design
    

    
    

37. Head First Design Patterns: A Brain-Friendly Guide
    
38. Design Patterns: Elements of Reusable Object-Oriented Software
    
39. Domain-Driven Design: Tackling Complexity in the Heart of Software
    
40. Domain-Driven Design Distilled
    
41. Design Patterns Explained: A New Perspective on Object-Oriented Design
    
42. Design Patterns in C# - Even though this is specific to C# the pattern can be used in any OO language.
    
43. Refactoring to Patterns
    
    

    Software Engineering Skill Sets
    

    
    

44. Building Microservices: Designing Fine-Grained Systems
    
45. Software Factories: Assembling Applications with Patterns, Models, Frameworks, and Tools
    
46. NoEstimates: How To Measure Project Progress Without Estimating
    
47. Object-Oriented Software Construction
    
48. The Art of Software Testing
    
49. Release It!: Design and Deploy Production-Ready Software
    
50. Working Effectively with Legacy Code
    
51. Test Driven Development: By Example
    
    

    Databases
    

    
    

52. Database System Concepts
    
53. Database Management Systems
    
54. Foundation for Object / Relational Databases: The Third Manifesto
    
55. Refactoring Databases: Evolutionary Database Design
    
56. Data Access Patterns: Database Interactions in Object-Oriented Applications
    
    

    User Experience
    

    
    

57. Don't Make Me Think: A Common Sense Approach to Web Usability
    
58. The Design of Everyday Things
    
59. Programming Collective Intelligence: Building Smart Web 2.0 Applications
    
60. User Interface Design for Programmers
    
61. GUI Bloopers 2.0: Common User Interface Design Don'ts and Dos
    
    

    Mentality
    

    
    

62. The Productive Programmer
    
63. Extreme Programming Explained: Embrace Change
    
64. Coders at Work: Reflections on the Craft of Programming
    
65. Facts and Fallacies of Software Engineering
    
    

    History
    

    
    

66. Dreaming in Code: Two Dozen Programmers, Three Years, 4,732 Bugs, and One Quest for Transcendent Software
    
67. New Turning Omnibus: 66 Excursions in Computer Science
    
68. Hacker's Delight
    
69. The Alchemist
    
70. Masterminds of Programming: Conversations with the Creators of Major Programming Languages
    
71. The Information: A History, A Theory, A Flood
    
    

    Specialist Skills
    

    
    In spite of the fact that many of these won't apply to your specific job I still recommend reading them for the insight, they'll give you into programming language and technology design.
    
    

72. Peter Norton's Assembly Language Book for the IBM PC
    
73. Expert C Programming: Deep C Secrets
    
74. Enough Rope to Shoot Yourself in the Foot: Rules for C and C++ Programming
    
75. The C++ Programming Language
    
76. Effective C++: 55 Specific Ways to Improve Your Programs and Designs
    
77. More Effective C++: 35 New Ways to Improve Your Programs and Designs
    
78. More Effective C#: 50 Specific Ways to Improve Your C#
    
79. CLR via C#
    
80. Mr. Bunny's Big Cup o' Java
    
81. Thinking in Java
    
82. JUnit in Action
    
83. Functional Programming in Scala
    
84. The Art of Prolog: Advanced Programming Techniques
    
85. The Craft of Prolog
    
86. Programming Perl: Unmatched Power for Text Processing and Scripting
    
87. Dive into Python 3
    
88. why's (poignant) guide to Ruby

Caclulus track is typically required. Linear algebra is pretty useful (and often required). If you really wanna go into CS specific maths.... pick up a book on Discrete Math and give it a go. If you want to be really hardcore, pickup Concrete Mathematics ... good luck, hard book.

Honestly, you're probably better off spending that time learning a programming language. Specifically, whatever language your school teaches mostly. Math in a CS bachelor isn't very intense until you get into senior/graduate level courses.

• A decent idea of how all the internal parts of a computer fit together. I'd recommend Computer Systems: A Programmer's Perspective and Code: The Hidden Language of Computer Hardware and Software
  
• A good book to solidify your principles like Code Complete or Pragmatic Programmer.
  
• Really understanding the nuts and bolts of a text editor that can preferably work with any language and is cross-platform (Emacs, Vim, Sublime Text to name a few)
  
• A good understanding of a version control system like Git. I'd recommend Git for Computer Scientists and Git from Bottom Up

Programming is language agnostic; it sounds like you're looking for breadth rather than depth, so:

• these books are free; they will teach you C++, including basic imperative and procedural programming, structured programming, pointer manipulation, and recursion;
  
  
• once you've got those down, this book will introduce you to higher order programming and macros, as implemented in C++; and,
  
  
• after you're familiar with those, this book will teach you the mathematics behind the design of the standard library for C++.
  
  Those are the only books I ever used, and I've had no problem programming in any (serious) language I've come across.
  
  Scala, Mozart, etc. cover more "programming paradigms" than C++, but there are more resources for C++ than those languages, so it is a good balance between breadth and support. If you would rather learn a few languages than one language then I would suggest the combination of an ML, C, Python, XSLT, and Scheme. Spend two weeks in each language and make sure you've implemented something nontrivial in each, and make sure that implementation is idiomatic.

There's also Knuth et al's Concrete Mathematics. The writing style is very loose and casual but it quickly moves from fairly easy intro level stuff to graduate level mathematics, so whether you find it useful as an intro book depends on your background. It is however, and excellent discrete book if you work through it slowly and methodically.

Check out The Annotated Turing by Charles Petzold. It's Turing's paper on the Entscheidungsproblem which introduces Turing Machines, annotated with a lot of background information and some stuff about Turing's career. Very interesting stuff.

I can also recommend Code, by the same author which describes how a computer works from basic principles. It's doesn't have a lot of material on Turing, but it's certainly an interesting read for anyone interested in Comp Sci.

I thought Coders at Work: Reflections on the Craft of Programming was a really enjoyable read.

It's just a collection of interviews. The book features some really interesting programmers such Ken Thompson, Joe Armstrong, Peter Norvig, and Donald Knuth. I had a great time reading their stories.

The "Spot the bug" posts here are like that although I think they are c++ (http://blogs.msdn.com/b/rsamona/).

Books like Writing Solid Code (http://www.amazon.com/Writing-Solid-Microsoft-Programming-Series/dp/1556155514) are also helpful if you're going to be writing a lot of C or C++ code. It has some helpful ideas about how to build C code that is debuggable.

Course: UC Berkeley OS & Systems Programming

The Art of Unix Programming

There are many similar resources out there. Extract keywords, web search, repeat. Best of luck!

Turing's Cathedral: The Origins of the Digital Universe https://www.amazon.com/dp/1400075998/ref=cm_sw_r_cp_api_i_AToIDb7FX1A9D

Its about the creation of the institue for advanced study with Von Neumann, Oppenheimer and the rest of them. Fascinating story about the politics around the creation of modern computer science.

The Annotated Turing is fantastic! Also check out Turing's Cathedral for some insight into how his 1936 paper influenced computing into the next few decades and The Essential Turing to read Turing in his own words.

For a look at how Turing influenced information theory (and a fascinating general introduction to its history), check out The Information.

If you only read one work on the topic, it should be The Art of Computer Programming by Don Knuth: https://www.amazon.com/dp/0321751043/

The textbook for MIT's 6.001 (introduction to computer science) is the much loved Structure and Interpretation of Computer Programs by Abelson, Sussman, and Sussman: https://www.amazon.com/dp/0262510871/ . Originally it was in Scheme but the 2nd edition is in Python.

Finally, because people asking about computer science are often asking about something a bit broader than pure computer science, I recommend Code: The Hidden Language of Computer Hardware and Software by Charles Petzold. It is a thorough tour of computing in practice at every level, top to bottom. https://www.amazon.com/dp/073560505X/

It seems that your comment contains 1 or more links that are hard to tap for mobile users.
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Thanks, I already have a book on this I was planning on reading: Introduction to Automata Theory, Languages, and Computation. I just started reading CLRS though, do you think it would be helpful to finish it or are the two mostly unrelated?

Logic, Number theory, Graph Theory and Algebra are all too much for you to handle on your own without first learning the basics. In fact, most of those books will probably expect you to have some mathematical maturity (that is, reading and writing proofs).

I don't know how theoretical your CS program is going to be, but I would recommend working on your discrete math, basic set theory and logic.

This book will teach you how to write proofs, basic logic and set theory that you will need: http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995


I can't really recommend a good Discrete Math textbook as most of them are "meh", and "How to Prove It" does contain a lot of the material usually taught in a Discrete Math course. The extra topics you will find in discrete maths books is: basic probability, some graph theory, some number theory and combinatorics, and in some books even some basic algebra and algorithm analysis. If I were you I would focus mostly on the combinatorics and probability.


Anyway, here's a list of discrete math books. Pick the one you like the most judging from the reviews:

• http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328
  
• http://www.amazon.com/Discrete-Combinatorial-Mathematics-Applied-Introduction/dp/0201726343
  
• http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073383090
  
• http://www.amazon.com/Discrete-Mathematics-Computer-Science-Solutions/dp/053449501X
  
• http://www.amazon.com/Mathematics-Discrete-Introduction-Edward-Scheinerman/dp/0840049420 (read the reviews of the previous edition: http://www.amazon.com/Mathematics-Discrete-Introduction-Edward-Scheinerman/dp/0534398987)
  
  
  Don't bother trying to learn too much too soon, as you really do need to let time for the math to sink in.

As someone who hated math, this turned out to be one of my absolute favourite books in college:

http://www.amazon.co.uk/gp/product/1408263238?psc=1&redirect=true&ref_=oh_aui_detailpage_o06_s00

Probably not what you're looking for though.

Are you looking for pure computer science or do programming books count?

The pragmatic programmer is a great book, and an enjoyable read:

http://www.amazon.co.uk/Pragmatic-Programmer-Andrew-Hunt/dp/020161622X/ref=sr_1_1?ie=UTF8&qid=1422386669&sr=8-1&keywords=pragmatic+programmer

Go read Cracking the Coding Interview. It covers pretty much everything they are likely to ask you and has a bunch of practice questions with solutions/rationale.

I read Computer Systems A programmer's perspective on my first BSc year in Software Engineering.

Start with the fundamentals so has a good foundation to build on

Thank you. I really want to go into the 'Curse the entire field of CS and maths' level. This is the book I was suggested via PM. I'll try the first approach you suggest, then I'll scale up since we are a small group of people trying to learn together so I think that a couple of heads tackling into a problem might solve it.