FUNDAMENTALS OF PRACTICAL COMPUTING Ken ChurchFUNDAMENTALS 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 to – 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 – Example: Use Google to figure out how to install R (a stat package) LISP ( 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 The On-Line Encyclopedia of Integer Sequences Eval

Sqrt(-1)  Error (for many tools)

Roots (without approximations)

Numerical Methods: Approximations such as Newton’s Method

Complex Roots

Newton’s Method

Newton’s Method

Symbolic Alternative

Symbolic Methods  Search

Recursion

(define (fact x) (if (<= x 1) 1 (* x (fact (- x 1))))) (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))))) More Recursion Lecture3/recursive_examples.lsp

The Roots of LISP Eval

Symbolic Differentiation

Symbolic Differentiation Lecture1/deriv.lsp

Syntax

Semantics

Surprise: Church’s Thesis

Effective Procedure – always give some answer – 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: Church's thesis – Effectively Procedure = Recursively Computable – Not a mathematical statement  No proof Church’s Thesis

Recursion & Factorial

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 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  Install (hint: Google) – R (a stat package) – LISP ( – cygwin (Unix for Windows); skip if you have Unix Send me an with: – Subject: Homework #1 from – 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 – 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?