Watch Mathematical Thinking in Computer Science | Discrete Mathematics for Computer Science Video Tutorial

About this Course Mathematical thinking is crucial in all areas of computer science: algorithms, bioinformatics, computer graphics, data science, machine learning, etc. In this course, we will learn the most important tools used in discrete mathematics: induction, recursion, logic, invariants, examples, optimality. We will use these tools to answer typical programming questions like: How can we be certain a solution exists? Am I sure my program computes the optimal answer? Do each of these objects meet the given requirements? --------- TIME STAMP --------------- MAKING CONVINCING ARGUMENTS 0:00:00 Promo video 0:01:15 Proofs 0:05:03 Proof by Example 0:06:54 Impossiblity proof 0:09:29 Impossibility proof, 2 and conclusion 0:13:22 One example is Enough 0:16:49 Splitting an octagon 0:18:13 Making Fun in real life Tensegrities (optional) 0:28:38 Know Your Rights 0:34:28 Nobody can win All the time Nonexisting Examples HOW TO FIND AN EXAMPLE? 0:42:55 Magic Squares 0:46:22 Narrowing the search 0:53:09 Multiplicative Magic Squares 0:58:26 More Puzzles 1:07:48 Integer linear Combinations 1:13:04 Paths in a Graph 1:17:39 Warm-up 1:23:02 Subset without x and 100-x 1:27:12 Rooks on a chessboard 1:29:52 Knights on a Chessboard 1:35:02 Bishop on a chessboard 1:37:45 Subset without x and 2x 1:44:09 N Queens Brute Force Search 1:54:41 N Queens Backtracking Example 2:02:01 N Queens Backtracking Code 2:09:35 16 Diagonals RECURSION AND INDUCTION 2:13:19 Recursion 2:23:05 Coin Problem 2:27:51 Hanoi Towers 2:35:17 Introduction,Lines and Triangles Problem 2:45:33 Lines and Triangle Proof by Induction 2:51:33 Connection Points 3:04:33 Odd Points Proof by induction 3:10:03 Sums of Numbers 3:18:55 Bernouli's Inequality 3:26:57 Coins Problem 3:36:42 Cutting a Triangle 3:45:23 Flawed Induction Proofs 3:54:51 Alternating Sum 4:04:00 Examples 4:10:44 Counterexamples 4:15:44 Basic Logic Constructs 4:26:43 If-Then Generalization, Quantification 4:34:54 Reductio ad Absurdum 4:39:26 Balls in Boxes 4:43:32 Numbers in Tables 4:49:06 Pigeonhole Principle 4:51:21 An (-1,0,1) Antimagic Square 4:53:53 Handshakes INVARIANTS 4:57:00 Double Counting 4:59:50 Homework Assignment'problem 5:01:28 Invariants 5:04:18 More Coffee 5:08:37 Debugging Problem 5:11:12 Termination 5:15:24 Atthur's Books 5:23:45 Even and odd Numbers 5:28:21 Summing up Digits 5:32:58 Switching Signs 5:36:17 Advance Signs Switching SOLVING A 15-PUZZLE 5:44:48 The rules of 15-puzzle 5:47:59 Permutations 5:57:07 Proof the Diffucult part 6:05:46 Mission Impossiple 6:08:14 Classify a Permutation as Even Odd 6:13:25 Bonus Track Fast Classification 6:15:20 Project The Task 6:16:52 Quiz Hint Why Every Even Permutation is Solvable In the course, we use a try-this-before-we-explain-everything approach: you will be solving many interactive (and mobile friendly) puzzles that were carefully designed to allow you to invent many of the important ideas and concepts yourself. Prerequisites: 1. We assume only basic math (e.g., we expect you to know what is a square or how to add fractions), common sense and curiosity. 2. Basic programming knowledge is necessary as some quizzes require programming in Python. ⭐ Important Notes ⭐ ⌨️ This course is created in collaboration with University of California SAN DIEGO discrete mathematics for computer science full course, discrete mathematics for computer science crash course, discrete mathematics for computer science course, discrete mathematics for computer science coursera, discrete math for computer science, discrete mathematics for computer science free course, introduction to discrete mathematics for computer science specialization, discrete mathematics for computer science tutorials, introduction to discrete mathematics for computer science, discrete mathematics for computer science youtube, discrete mathematics computer science #mathematicalthinking #computersceince computer science, math, mathematics, math for computer science, how much math do computer scientists use, how much math is needed for computer science, math major, computer science major, graph theory, number theory, proofs, computer science math, college math, discrete math, how much math is in computer science,