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 Kenneth.Church@jhu.edu– 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 (Kenneth.Church@jhu.edu)

– 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 Sequenc

es• Eval

Sqrt(-1) Error (for many tools)

Roots (without approximations)2/)51( x

Numerical Methods:Approximations such as Newton’s Method

Complex Roots

Newton’s Methodhttp://archives.math.utk.edu/visual.calculus/3/newton.5/

1 3 5 7 9 11 13 152.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

sqrt(5)

Iteration (n)

Estim

ate

of s

qrt(

5)

Newton’s Methodhttp://archives.math.utk.edu/visual.calculus/3/newton.5/

1 2 3 4 5 6 7 8 9 10 11 12 13 14 152.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

-5

0

5

10

15

20

sqrt(5) sqrt(-5)

Iteration (n)

Estim

ate

of s

qrt(

5)

Estim

ate

of s

qrt(

-5)

Symbolic Alternative

1 3 5 7 9 11 13 152.22.32.42.52.62.72.82.9

3

-5

0

5

10

15

20

sqrt(5) sqrt(-5)

Iteration (n)

Estim

ate

of s

qrt(

5)

Estim

ate

of s

qrt(

-5)

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 RecursionLecture3/recursive_examples.lsp

The Roots of LISPEval

Symbolic Differentiation

Symbolic DifferentiationLecture1/deriv.lsp

http://mitpress.mit.edu/sicp/full-text/sicp/book/node39.html

Syntaxhttp://www.allisons.org/ll/FP/Lambda/

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:– Effectively Procedure = Recursively Computable – Not a mathematical statement No proof

Church’s Thesishttp://en.wikipedia.org/wiki/Effectively_calculable

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 Sequenc

es• 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 Kenneth.Church@jhu.edu

• 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(4) 2 v. sqrt(4) -2– Are there any settings so that sqrt(4) 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 & Encyclopedia 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?