CS 131 Spring 2018 - List of topics
See lecture recordings here. Warning: they are low-resolution and not great audio quality, so they do not substitute for coming to lecture, but they can be helpful is you must miss a class.
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Jan 23
- Welcome to CS 131
- Propositional logic
- Propositions and logical equivalence
- Evaluating compound propositions
- Conditional statements
- Logical equivalence
- Laws of propositional logic
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Jan 25
- Boolean algebra
- Intro
- Boolean functions
- CNF / DNF
- Boolean algebra
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Jan 30
- Boolean algebra
- Functional completeness
- Boolean satisfiability
- Boolean algebra
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Feb 1
- Predicates and first order logic
- Predicates and quantifiers
- Quantified statements
- Predicates and first order logic
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Feb 6
- Predicates and first order logic
- Nested quantifiers (two chapters)
- Rules of inference with quantifiers
- Predicates and first order logic
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Feb 8
- Sets
- Sets and subsets
- Sets of sets
- Union and intersection
- More set operations
- Set identities
- Cartesian products
- Partitions
- Sets
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Feb 13
- See lecture notes
- Functions (whole zyBooks chapter)
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Feb 15
- Relations (whole zyBooks chapter)
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Feb 20
- Monday schedule
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Feb 22
- Proofs (whole zyBooks chapter)
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Feb 27
- More on proofs
- More on proof by cases
- Euclid algoritm
- GCD
- Theorem about GCD (why Euclidian algorithm return GCD) and its proof
- Theorem: GCD of two numbers over their GCD is 1 (and its proof)
- More on proofs
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Mar 1
- Writing GCD formal defintion in a form of conjunction of three statememnts
- Theorem: any rational number can be written as x over y s.t. GCD(x,y)=1 (and its proof)
- Applying GCD to rational numbers (hint: multiply by denominators)
- Proof that square root of 2 is irrational
- Theorem: any integer greater than 1 is divisible a prime (and its proof)
- Theorem: there are infinitely many primes (and its proof)
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Mar 20
- Halting problem
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Mar 27
- Geometric series
- Inductive proofs that are not sums
- Graphs (some basic definitions)
- "All horses are the same color"
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Mar 29
- Sum of infinite series (r < 1)
- False proofs of horses color
- Fiboncci sequence
- Analusis of Euclid's algorithm (see notes)
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April 3
- Loop invariants
- Pre / post conditions as ways to reason about program correctness
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April 5
- Structural induction
- General (non-binary) trees
- Boolean formulas
- Proof via structural induction
- In any tree the number of edges is one smaller than the number of nodes
- In any formula number of opening and closing patterns matches
- Two recursive algorithms
- Structural induction
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April 17 / 19
- Binomial coefficients
- Relation between inclusion / exclusion and identity
- Binomial distribution
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April 20
- Binomial coefficients
- Pascal's triangle
- Binomial recurrence with code
- Probability basics: sample spaces, outcomes, events, etc
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April 25
- Bernoulli trials and binomial distribution
- Visualization
- Not in the book
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Thu Apr 27:
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Not in the book
- If you try to estimate the bias of a coin (for example, in public polling or in Monte Carlo simulation) by doing
$n$ independent samples, your answer will very likely be within about$\frac{1}{\sqrt{n}}$ of the correct answer. So need$n = 400$ samples to get to within 5%,$n = 1112$ to get within 3%,$n = 10000$ to get within 1%.
- If you try to estimate the bias of a coin (for example, in public polling or in Monte Carlo simulation) by doing
- Conditional probability and independence
- Random variables and expectations
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Not in the book