Life of Fred: Metamathematics
ISB: 978-1-937032-63-0, hardback, 128 pages.
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List of Topics Covered:
The subfields of math. Turing machines definition. Adding, subtracting, recognizing more than two symbols. The impossibility of locating all the non-blank symbols on an input tape. Turing machines with two tracks. With two tapes. Unary notation. The universal computer. Turing machines on an infinite checkerboard instead of a tape. The halting problem. Dealing with negative numbers, copying a number, multiplying, exponentiation, projection and constant functions, determining if x > y. Doing logic computations. Doing geometry. True vs. provable. Gödel's First and Second Incompleteness Theorems. Computable functions defined. The Church-Turing thesis. Primitive recursive functions. General recursive functions. The Ackermann function. Self-replicating machines. P and NP functions.
The full 10-book Extra High School and College Math series includes:
- Life of Fred: Logic
- Life of Fred: Calculus Expanded Edition (freshman and sophomore year of college)
- Life of Fred: Statistics Expanded Edition
- Life of Fred: Life of Fred: Five Days of Upper Division Math: Set Theory, Modern Algebra, Abstract Arithmetic, Topology
- Life of Fred: Abstract Algebra
- Life of Fred: Linear Algebra Expanded Edition (junior year of college)
- Life of Fred: Real Analysis
- Life of Fred: Complex Analysis
- Life of Fred: Numerical Analysis
- Life of Fred: Metamathematics
Life of Fred: Chemistry can also be read near the end of High-School or early College.