Reading Log

• January 7, 2015: Why Discrete Mathematics
  • Robert H. Lewis, What Math? The Most Misunderstood Subject
    "Today, mathematics as a mode of thought and expression is more valuable than ever before. Learning to think in mathematical terms is an essential part of becoming a liberally educated person."
  
  
  • Keith Devlin, Why universities require computer science students to take math: Introduction
    "The main benefit of learning and doing mathematics is that it develops the ability to reason about formally defined abstract structures like those in computer science and its applications."
    "Once we have learned how to reason precisely about one set of abstractions, it takes relatively little extra effort to reason about any others."
    "Once you realize that computing is all about constructing, manipulating, and reasoning about abstractions, it becomes clear that an important prerequisite for writing (good) computer programs is the ability to handle abstractions in a precise manner. As it happens, that is something we humans have been doing successfully for more than three thousand years. We call it mathematics."
    "The truth is, of course, that computer science is entirely about abstractions."
  
  
  • Kim B. Bruce, Robert L. Scot Drysdale, Charles Kelemen, Allen Tucker, Why math?
    "The mathematical thinking, as well as the mathematics, in a computer science education prepares students for all stages of system development, from design to the correctness of the final implementation."
  
  
  • PETER B. HENDERSON, Mathematical reasoning in software engineering education
    "Discrete mathematics, especially logic, plays an implicit role in software engineering similar to the role of continuous mathematics in traditional physically based engineering disciplines."
  
  
  • Theresa Beaubouef, Why computer science students need math?
  
  
  • Jeff Kramer, Is abstraction the key to computing
    "My experience is that the better students are clearly able to handle complexity and to produce elegant models and designs. The same students are also able to cope with the complexities of distributed algorithms, the applicability of various modeling notations, and other subtle issues."
  
  
  • Edsger W. Dijkstra, Mathematical Methodology, Spring 1997
    "You will be treated as grown-ups, i.e. it is your responsibility to check that you understand what is going on in class. If I use a word you don't recognize or a sentence you cannot attach a meaning to, it is your duty to ask for clarification. If I go too fast, it is your duty to slow me down."
    "I intend to present mathematics not as the "abstract science of space, number, and quantity" (C.O.D.) but as the art and science of effective reasoning. (This view is not new, for it had its champions in the 19th century; it is not universally adopted either, as was shown recently by the anonymous referee who wrote "simplicity is not a scientific concern".)
    I expect to cover roughly 3 areas.
    (i) the structure of the highly effective argument without avoidable complications
    (ii) the design, with a minimum of detours, of such crisp arguments
    (iii) the adequate presentation of such arguments."
  • Edsger W. Dijkstra, Honors course "Mathematical Methodology", Spring 1996
    "This course is not about mathematical results but about doing mathematics, about wasting neither your own time, nor the time of your readers. Mathematics will be treated as the art and science of effective reasoning, the latter encompassing the design, recording and explanation of arguments."
  • Edsger W. Dijkstra, Introducing a course on mathematical methodology
  
  
• January 9, 12, 14, 16, 2015: Logic
  • Chapter 1 of the Textbook
  
  
  • Wikipedia, Barber paradox. See also: Page 16, question 50 of the Textbook.
  • Wikipedia, Liar paradox.
  
  
  • Wikipedia, Functional completeness.
    "In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is { AND, NOT }, consisting of binary conjunction and negation. The singleton sets { NAND } and { NOR } are also functionally complete."
  
  
  • John F. Halpin, Truth Functionality and non-Truth Functional Connectives
  
  
  • Larry W. Cusick, How To Write Proofs
  
  
  • Julian H. Gibbs, A Guide to Proof Strategies
  
  
• January 19, 21, 23, 2015: Sets
  January 26, 28, 2015: Functions
  January 28, 30, 2015: Sequences and summations
  
  • Chapter 2 of textbook
  
  
  • Wikipedia, Fibonacci number
  • MATHisFUN, Fibonacci Sequence
  
  
  • NRICH team, Clever Carl
    "One day Gauss' teacher asked his class to add together all the numbers from 1 to 100, assuming that this task would occupy them for quite a while. He was shocked when young Gauss, after a few seconds thought, wrote down the answer 5050."
  
  
• Feburary 2, 4, 6, 9, 11, 13, 23, 2015: Relations
  
  • Chapter 9 of textbook
  
  
  • Wikipedia, Lattice (order)


• Feburary 25, 27 (mid-term 1), March 2, 4, 2015: Number theory
  
  • Chapter 4 of textbook
  
  
  • Wikipedia, Positional notation


• March 6, 9, 11, 13, 2015: Induction and Recursion
  
  • Chapter 5 of textbook


• March 13, 16, 18, 20, 2015: Graphs
  
  • Chapter 10 of textbook
  
  
  • Tim Berners-Lee, How It All Started (A story of WWW).
  
  
  • Eric Steven Raymond, The Art of Unix Programming,
  
  
  • Google, Ten things we know to be true