CPSC 121: Models of Computation 2018 Summer Term 1 Introduction & Motivation Cinda Heeren, based on notes by Steve Wolfman, Patrice Belleville and others 1 This work is licensed under a Creative Commons Attribution 3.0 Unported License.
Learning Goals: In-Class By the end of the unit, you should be able to: – Give an example of how we can apply formal reasoning and computers to a simple, real- world task. – Give an example of how a computational solution to a simple task might go wrong. – Describe the two “big stories” of CS121: reasoning about computation and building computers. 2
Outline • Introductions • Introductions Exercise • The CS121 Story • Course Administration • Demo • Next Lecture Notes 3
Introductions Cinda Heeren <cheeren@cs.ubc.ca> ICICS 233 – OH: Mon Wed 2:30-4p LOTS of TAs! 4
Outline • Introductions • Introductions Exercise • The CS121 Story • Course Administration • Demo • Next Lecture Notes 5
More Introductions Introduce yourselves… how ? 6
Introduce Yourselves… FIND ~3 people around you, preferably people you’ve never met. Form a group. Have everyone in the group introduce themselves to everyone else in the group. (Count the number of intros this takes.) Tell everyone why you’re here, your favorite career that you’ll never have, and one unusual thing about you. BUT, tell two truths and a lie! 7
How Many Introductions? Problem : How many introductions does it take for everyone in a group to meet everyone else in a group? 8
Concept Q: Intros for 4 How many introductions does a group of 4 people take? a. 3 b. 4 c. 6 d. 12 e. None of these 9
How Many Introductions? Problem : How many introductions does it take for everyone in a group to meet everyone else in a group? To solve this problem, we need to model it more formally. 10
How Many Introductions? Model: One “introduction” is one person introducing themselves to another person. (Two people need two introductions to introduce themselves to each other.) A group has “introduced themselves” when every group member has introduced themselves to every other member. (No self-introductions!) Hi, I’m Hi Grace, Intro #1 Grace H. I’m Alan T. 11 Intro #2
How Many Introductions? Problem: How many introductions does it take for a group of n people to introduce themselves? 12
How Many Introductions? Our examples. Should 0 and 1 be examples? For 2 people? For 3 people? For 4 people? For 5 people? … For n people? 13
How Many Introductions? For 100 people? For 8675309 people? For 1526097757 people?
Program for Introductions int introductions(int n) { return _____________; } (in Java) (define (introductions n) ____________ ) (in Racket) 15
Program for Intros: Testing Java version with 100: 9900 Do you believe it? 16
Program for Intros: Testing Java version with 100: 9900 Java version with 8675309: 265642364 Do you believe it? 17
Program for Intros: Testing Java version with 100: 9900 Java version with 8675309: 265642364 Java version with 1526097757: -645820308 Um.. Do you believe it? 18 Does this fit with your “model” of computation?
Program for Intros: Testing Racket version with 100: 9900 Racket version with 8675309: 75260977570172 Racket version with 1526097757: 2328974362394333292 Do you believe it? 19 Will Racket always get the right answer?
Alternate Intros Program ;; Model in math, translate to Racket. (define (introductions n) (* n (- n 1))) ;; Model as “I know what happens ;; a) in a group of 0 people, and ;; b) when someone new enters a group.” ;; Translate to Racket. (define (introductions n) (if (= n 0) _______ ____________________ ; soln on smaller instance ____________________); + the extra intros 20 Are both correct?
Outline • Introductions • Introductions Exercise • The CS121 Story • Course Administration • Demo • Next Lecture Notes 21
Questions that CPSC121 Answers… How can we prove that our formula for the number of introductions is correct? What went wrong in our Java implementation but right in Racket? How does the computer (or DrRacket) decide if the characters of your program represent a name, a number, or something else? How does it figure out if you have mismatched " " or ( )? How do we model and reason about computational systems at various levels of abstraction? 22
CPSC 121: The Big Stories Theory Hardware How do we model How do we build devices computational systems that can compute out of (programs/computers) in real materials (“sand and order to design and rocks and water”)? analyze them? Grand goal : break Grand goal : Reason about down a full computer what is and isn’t into simple “gates”. possible to compute. Bonus end goal : Develop tools to communicate computational ideas clearly and precisely. 23
Our Working Computer 24 The whole thing (mostly wires connecting boxes).
Working Computer—zoomed in on one box Just the “ALU” (Arithmetic/Logic Unit). You’ll see a 25 pared-down version in lab in a couple of weeks.
CPSC 121: The (By?)Products Theory Hardware Products: Products: • Propositional logic • Gates • Predicate logic • Combinational circuits • Sets and functions • Binary data representations • Proof techniques ( especially induction!) • Sequential circuits • Finite Automata/Regular • A full computer Expressions • Universal machines • Uncomputability 26
What is CPSC 121 Good For? With CPSC121’s help, you will be able to: • model important problems so that they are easier to discuss, reason about, solve, and test. • learn new modeling formalisms more easily. • communicate clearly and unambiguously with other CS experts on complex topics. • characterize algorithms (CS problem solutions), such as proving their correctness or comparing their performance. • critically read proofs: justifying why each step is correct and judging what the proof means. 27
Outline • Introductions • Introductions Exercise • The CS121 Story • Course Administration • Demo • Next Lecture Notes 28
Course Administration Explore the CPSC 121 website: http://www.ugrad.cs.ubc.ca/~cs121/ Graded components: Pre-class quizzes (10) HW (5) Labs (9) Tutorials (9) Clickers Exams (3) 29
Announcements Quiz 1: av on Canvas. Due 5/16, noon. HW1: av 5/17. Due 5/24, 11:59p. Labs and tutorials start tomorrow, 5/15. Join Piazza – piazza.com/ubc.ca/summer2018/cpsc121 30
Outline • Introductions • Introductions Exercise • The CS121 Story • Course Administration • Demo • Next Lecture Notes 31
What Works is NOT Always Obvious Let’s try out what we’ll call the “Radix” Algorithm. General form: 1. Assemble some items (numbers or words) together in a list 2. Make an empty list for each possible value of each “digit” in the items (or letter in a word, etc.). 3. For each digit of the items in the main list, starting with the rightmost: a) For each item in the main list, in order: Put it at the back of the list indicated by the current digit in that item b) For each digit list, in order: Put the list at the back of the main list. What does this do? 32 How does it work?
What Doesn’t Work is Not Always Obvious Class Main { public static void main(String[] args) { // Let's add up 4 quarters. System.out.println("4 quarters gives us:"); System.out.println(0.25 + 0.25 + 0.25 + 0.25); // Let's do something a hundred times. int i = 100; do { // Make i one smaller. i--; } while (i > 0); System.out.println("Done!"); System.out.println("i ended up with the value: " + i); System.out.println("It went down by: " + (100 - i)); } } 33 https://repl.it/@ckh205/cpsc121-intro
What Doesn’t Work is Not Always Obvious Class Main { public static void main(String[] args) { // Let's add up 10 dimes. System.out.println("10 dimes gives us:"); System.out.println(0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1); // Let's try do something a hundred times.. // but accidentally go forever int i = 100; do { // Make i one LARGER. Oops! i++; } while (i > 0); System.out.println("Done!"); System.out.println("i ended up with the value: " + i); System.out.println("It went down by: " + (100 - i)); } 34 }
Even Bigger Story: __________ Computer Science is the science of “clear thought”, but not like philosophy (or religion, or poetry, or...). CS is the science of thoughts so clear in their expression and intent that we can realize them: execute them or test their truth in the world. CPSC121 provides and applies the fundamentals you need to model the world with “clear thought”. 35
Learning Goals: In-Class By the end of the unit, you should be able to: – Give an example of how we can apply formal reasoning and computers to a simple, real- world task. – Give an example of how a computational solution to a simple task might go wrong. – Describe the two “big stories” of CS121: reasoning about computation and building computers. 36
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