• Proofs and Fundamentals: A First Course in Abstract Mathematics, Ethan D. Bloch
• The Nuts and Bolts of Proof, Antonella Cupillari
  
• An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, Peter J. Eccles
• The Fundamentals of Higher Mathematics, Neil Falkner
• Math Proofs Demystified, Stan Gibilisco
• A Handbook of Writing for the Mathematical Sciences, Nicholas J. Higham
  
• A Primer of Mathematical Writing, Steven G. Krantz
  
• Theory and Problems of Set Theory and Related Topics (Schaum's Outline), Lipschultz
• How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, Daniel Solow
• Transition to Advanced Mathematics, Richard St. Andre (1971 PhD graduate of Ohio State!), D. Smith, and M. Eggen), Brooks/Cole Publishing Co., Pacific Grove, CA., Fifth edition, January, 2001
  
• The Foundations of Mathematics, Stewart and Tall
  
• How to Prove It: A Structured Approach, Daniel J. Velleman
• Schaum's Outline of Advanced Calculus, Second Edition, Robert C. Wrede and Murray Spiegel

Calculus help:

• The Calculus Lifesaver, Adrian Banner