An Introduction to Functional Programming Through Lambda Calculus by Greg Michaelson is a great intro book about both lambda calculus and functional programming that may be easier to digest: http://www.amazon.com/Introduction-Functional-Programming-Calculus-Mathematics/dp/0486478831. Also, it seems, available for free as a PDF: https://www.cs.rochester.edu/~brown/173/readings/LCBook.pdf

I found the book An Introduction to Functional Programming Through Lambda Calculus (Greg Michaelson, '88) a great resource. The first few sections give a nice, relatively gentle overview of the Lambda Calculus.

There is (oddly) also a well-formatted kindle version: https://www.amazon.com/Introduction-Functional-Programming-Calculus-Mathematics/dp/0486478831

I recommend the book the book "Introduction ot functional programming through the lambda calculus"

http://www.amazon.com/Introduction-Functional-Programming-Calculus-Mathematics/dp/0486478831

EDIT: spelling error

I've taken a look at your github profile and if your university is anything like mine you're most likely going to be miles ahead of your peers to start with. Don't be surprised if none of your classmates know anything about how to use version control or anything more than the basics or web programming or python.

For free ebooks that center around a specific language you should check out this website.

As for the maths side of things:

Discrete Mathetics:

• Discrete Mathematics (May be overkill if your course was as simple as mine)
  
  
• Concrete Mathematics (I would have failed my math courses if not for this one)
  
  
• Computational Discrete Mathematics (Another good online course)
  
  

  Formal Specification:
  

  
  

• The Essence of Z
  
  
• The Z Notation: A Reference Manual (Free)
  
  

  Foundations of Computing (Turing Machines, Set Theory, Problem Theory):
  

  
  

• An Introduction to Functional Programming Through Lambda Calculus
  
  
• CS103 - Stanford University This is an online course but the materials are just as good as any textbook.
  
  It's a lot of absorb but you've got a few years,

An Introduction to Functional Programming Through Lambda Calculus

a beginner level book; helped me when i started looking into FP & Lambda calculus.

http://www.amazon.com/Introduction-Functional-Programming-Calculus-Mathematics/dp/0486478831

I liked this book: https://www.amazon.com/Introduction-Functional-Programming-Calculus-Mathematics/dp/0486478831

Despite its programming language focus I think it has what you want: clear explanations and lots of exercises with solutions.

This is a great book, if you have some (basic) programming background and want to learn more about the programming languages' "relations" to different kinds of applications, systems and computers: Programming Languages: Principles and Paradigms (Undergraduate Topics in Computer Science).

If you already know some programming, but never heard/read/learned about the Functional Paradigm (specially with Lambda Calculus): An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics).

If you've got some experience with Imperative Programming, and would like to learn a really powerful and versatile Functional Programming language (Haskell), this book is considered as the best beginner's guide: Learn You a Haskell For Great Good!: A Beginner's Guide. I believe it's digital (online) version is available for free at their official website http://www.learnyouahaskell.com.