600.103 FUNDAMENTALS OF PRACTICAL COMPUTING Ken Church • Intended audience: – Students considering a major in • science, engineering or medicine • Small Class • Diversity: Geeks Mainstream – like Calculus &“typing” – College High School Elementary School – Fun (not too much work) Sell the field • Practical: – Please bring laptops to class if you can • Familiarize students with lots of stuff (breadth) • Not just a single programming language (not depth) • Fundamentals: – Lots more to Computer Science than hacking Teamwork, Web-work, etc. • Encourage teamwork, Google, Wikipedia, etc. • Homework: – Submit by email to [email protected] – Due Tuesday morning at sunrise • So I have time to adjust my Tuesday lectures (if necessary) – Target: 2 hours per hour of class • 1 hour installing software, plus • 1 hour of exercises (as opposed to problem sets) – Homework comes with hints (as opposed to recipes) • Feel free to ask for more hints ([email protected]) – Example: Use Google to figure out how to install • R (a stat package) • LISP (http://www.newlisp.org/) • cygwin (Unix for Windows) Cheating • Please don’t, but if you do, you are only cheating yourself • I want to encourage teamwork & web-work – Because they are great ways to learn – “Although you may work in small groups, each student must submit his/her own program and the code may not be a copy of others’ code. You may share ideas and help – but you must write your own code and your assignment MUST be SUBSTANTIALLY different from all others.” – Ok to submit a team effort (especially if you tell me who you are working with) • If you can’t do the homework, explain why – My bad – Software package doesn’t work for your machine – I asked for more than 2 hours (feel free to stop after 2 hours) • Homework is for your benefit (and mine) • Homework will be graded: satisfactory (or not) • Exams (mid-term & final) Grades – Goal: Learn from the homework You’ll do fine on the exams First Four Weeks • Symbolic Programming (how CS was taught in 1970s) – Practical: Familiarize students with stat package(s), • As well as symbolic alternatives: LISP & Wolfram Alpha – Fundamental: • Stuff you can’t do with your favorite stat package • LISP: Recursion, Eval, Symbolic Differentiation • Lambda Calculus (“Small is Beautiful” beyond reason; Church’s Thesis & Computability) • Unix for Poets (“Small is Beautiful”) – How to program (without realizing that it is programming) – How to use tr, awk & those other crazy Unix utilities (pipes) – Examples: count words (and ngrams); find interesting word associations. • More Unix for Poets • Python & NLTK (Natural Language Toolkit): – Unix for Poets (without Unix) – Formal Language Theory & Chomsky Hierarchy Symbolic Features (Bet you can’t do this with your favorite statistics package) • Complex Numbers: Sqrt(-1) • Roots (without approximations) • Differentiation (without approximations) • Integration (without approximations) • The On-Line Encyclopedia of Integer Sequences • Eval Sqrt(-1) Error (for many tools) Roots (without approximations) x ( 1 5) / 2 Numerical Methods: Approximations such as Newton’s Method Complex Roots Newton’s Method http://archives.math.utk.edu/visual.calculus/3/newton.5/ sqrt(5) 3 2.9 2.8 2.7 2.6 2.5 Estimate of sqrt(5) Estimate 2.4 2.3 2.2 1 3 5 7 9 11 13 15 Iteration (n) Newton’s Method http://archives.math.utk.edu/visual.calculus/3/newton.5/ 3 16 14 2.9 12 2.8 10 5) - 2.7 8 6 2.6 4 2.5 2 Estimate of sqrt(5) Estimate 0 2.4 of sqrt( Estimate -2 2.3 -4 2.2 -6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Iteration (n) sqrt(5) sqrt(-5) 3 20 5) - 2.8 15 Symbolic 10 2.6 5 Alternative 2.4 0 Estimate of sqrt(5) Estimate 2.2 -5 of sqrt( Estimate 1 3 5 7 9 11 13 15 Iteration (n) sqrt(5) sqrt(-5) Symbolic Methods Search Recursion (define (fact x) (if (<= x 1) 1 (* x (fact (- x 1))))) More Recursion Lecture3/recursive_examples.lsp (define (fib x) (if (<= x 2) 1 (+ (fib (- x 1)) (fib (- x 2))))) (define (len x) (if (empty? x) 0 (+ 1 (len (rest x))))) (define (rev x) (if (empty? x) x (append (rev (rest x)) (list (first x))))) The Roots of LISP Eval Symbolic Differentiation Symbolic Differentiation Lecture1/deriv.lsp http://mitpress.mit.edu/sicp/full-text/sicp/book/node39.html Syntax http://www.allisons.org/ll/FP/Lambda/ Semantics Surprise: Church’s Thesis • Effective Procedure Church’s Thesis – always give some answer http://en.wikipedia.org/wiki/Effectively_calculable – always give the right answer – always be completed in a finite number of steps – work for all instances of problems of the class • Recursively Computable – Three definitions later found to be equiv to one another • general recursion • Turing machines • λ-calculus • Church's thesis: – Effectively Procedure = Recursively Computable – Not a mathematical statement No proof Recursion & Factorial http://www.allisons.org/ll/FP/Lambda/Introduction/ Summary: Symbolic Features (Bet you can’t do this with your favorite statistics package) • Complex Numbers: Sqrt(-1) • Roots (without approximations) • Differentiation (without approximations) • Integration (without approximations) • The On-Line Encyclopedia of Integer Sequences • Eval First Four Weeks • Symbolic Programming (how CS was taught in 1970s) – Practical: Familiarize students with stat package(s), • As well as symbolic alternatives: LISP & Wolfram Alpha – Fundamental: • Stuff you can’t do with your favorite stat package • LISP: Recursion, Eval, Symbolic Differentiation • Lambda Calculus (“Small is Beautiful” beyond reason; Church’s Thesis & Computability) • Unix for Poets (“Small is Beautiful”) – How to program (without realizing that it is programming) – How to use tr, awk & those other crazy Unix utilities (pipes) – Examples: count words (and ngrams); find interesting word associations. • More Unix for Poets • Python & NLTK (Natural Language Toolkit): – Unix for Poets (without Unix) – Formal Language Theory & Chomsky Hierarchy Homework: Questions [email protected] • Install (hint: Google) – R (a stat package) – LISP (http://www.newlisp.org/) – cygwin (Unix for Windows); skip if you have Unix • Send me an email with: – Subject: 600.103 Homework #1 from <name> – Body: screen shots (see next couple of slides) – Due Tuesday morning (at sunrise) Homework: sqrt(4) • Screenshots of sqrt(4) and sqrt(-4) from – R – Wolfram Alpha – Newton’s Method http://archives.math.utk.edu/visual.calculus/3/newton.5 – LISP • For Newton’s Method, what settings generate – sqrt(2) 2 v. sqrt(2) -2 – Are there any settings so that sqrt(2) NaN? • In R, show me the following plot – x = seq(-4,4,1/10) – plot(x, x^2 - 4) – abline(h=0) – abline(v=c(-2,2), col="red") Fibonacci • Use NewLisp & Encylopedia of Integer Sequences to compute Fibonacci – F(n) = F(n-1) + F(n-2), F(0)=F(1)=1 – What is F(15)? Readings • The Roots of LISP – Use Google to find the article – “The unusual thing about Lisp-- in fact, the defining quality of Lisp-- is that it can be written in itself.” • The Halting Problem (Wikipedia) – What does this have to do with Computability?.