You will study logic and set theory in an introductory discrete mathematics. The concepts you learnt here will play a key role in your later studies and improve your thinking skill. You will also study proofs, functions (injective, surjective, bijective inverse), introductory graph theory and number theory, Euclid's algorithm, discrete probability (counting, nCr, nPr) etc in this course.
Only for Proof, Logic and Set Theory:
- Connell E.H. Background and Fundamentals of Mathematics [.pdf] (FREE!) - A short chapter from the author's algebra book.
- Copi I.M. and Cohen C. Introduction to Logic
- Daoud A. and Franklin J. Proof in Mathematics: An Introduction
- Düntsch I. Sets, Relations, Functions (FREE!)
- Enderton H.B. Elements of Set Theory
- Halmos P.R. Naive Set Theory - Don't misinterpret the word naive, though he propose the honest title as An Outline of the Elements of Naive Set Theory. This is not those books for dummies nor complete idiot's guide. Set theory plays a significant role in mathematics, if you are serious about it. Halmos is one of the better expositors of mathematics.
- Halmos P.R. and Givant S. Logic as Algebra
- Hurley P.J. A Concise Introduction to Logic
- Ikenaga B. Notes on Math Proof (FREE!)
- Skolem T.A. Abstract Set Theory (FREE!)
- Suppes P. Introduction to Logic
- Velleman D.J. How to Prove It: A Structured Approach - Let me warn you: proof is a crucial, I repeat, crucial, part in higher mathematics. Velleman did a good job for beginners here.
In general:
- Anderson I. A First Course in Discrete Mathematics
- Chen H.T. Discrete Mathematics (see the Lecture Notes section) (FREE!)
陳旭東：離散數學 - Chen W.W.L. Discrete Mathematics (FREE!)
- Epp S.S. Discrete Mathematics with Applications - I enjoy reading Epp's text when I first learn this topic. At this stage, some author makes good effort to spark student's interest. Don't forget to check out the errata.
- Finan M.B. Lectures Notes in Discrete Mathematics [.pdf] (FREE!)
- Graham R.L., Knuth D.E. and Patashnik O. Concrete Mathematics: A Foundation for Computer Science
- Kemeny J.G., Snell J.L. and Thompson G.L. Introduction to Finite Mathematics (FREE!)
- Lerma M.A. Notes on Discrete Mathematics [.pdf] (FREE!)
- Lovasz L., Pelikan J. and Vesztergombi K.L. Discrete Mathematics
- Lovasz L. and Vesztergombi K. Discrete Mathematics [.pdf] (FREE!)
- MacGillivray G UVic Discrete Mathematics Study Guide (FREE!)
- Rosen K.H. Discrete Mathematics and Its Applications - Another nice introductory text on this topic. See the companion website.
- Ross S.M. Topics in Finite and Discrete Mathematics
- Santos D. Discrete Maths Lecture Notes [.pdf] (FREE!)
Santos D. Discrete Maths II [.pdf] (FREE!) - Simonson S. Discrete Mathematics (FREE!) - Includes lecture videos.
- Sutner K. Computational Discrete Mathematics (FREE!)
- 國立交通大學：離散數學課程講義 (FREE!)
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