Mathematical Thinking in Computer Science
- Offered byCoursera
Mathematical Thinking in Computer Science at Coursera Overview
Duration | 41 hours |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Beginner |
Official Website | Explore Free Course  |
Credential | Certificate |
Mathematical Thinking in Computer Science at Coursera Highlights
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Course 1 of 5 in the Introduction to Discrete Mathematics for Computer Science Specialization
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Beginner Level
- Approx. 41 hours to complete
- English Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish
Mathematical Thinking in Computer Science at Coursera Course details
- 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?
- 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.
Mathematical Thinking in Computer Science at Coursera Curriculum
Making Convincing Arguments
Promo Video
Proofs?
Proof by Example
Impossibility Proof
Impossibility Proof, II and Conclusion
One Example is Enough
Splitting an Octagon
Making Fun in Real Life: Tensegrities (Optional)
Know Your Rights
Nobody Can Win All The Time: Nonexisting Examples
Active Learning
Python Programming Language
Slides
Slides
Acknowledgements
Puzzle: Tile a Chessboard
Tiles, dominos, black and white, even and odd
Puzzle: Two Congruent Parts
Puzzle: Splitting
How to Find an Example?
Magic Squares
Narrowing the Search
Multiplicative Magic Squares
More Puzzles
Integer Linear Combinations
Paths In a Graph
Warm-up
Subset without x and 100-x
Rooks on a Chessboard
Knights on a Chessboard
Bishops on a Chessboard
Subset without x and 2x
N Queens: Brute Force Search
N Queens: Backtracking: Example
N Queens: Backtracking: Code
16 Diagonals
Slides
Slides
N Queens: Brute Force Solution Code
N Queens: Backtracking Solution Code
16 Diagonals: Code
Slides
Puzzle: Magic Square 3 times 3
Puzzle: Different People Have Different Coins
Puzzle: Free Accomodation
Is there...
Maximum Number of Two-digit Integers
Maximum Number of Rooks on a Chessboard
Maximum Number of Knights on a Chessboard
Maximum Number of Bishops on a Chessboard
Subset without x and 2x
Puzzle: N Queens
Puzzle: 16 Diagonals
Number of Solutions for the 8 Queens Puzzle
Recursion and Induction
Recursion
Coin Problem
Hanoi Towers
Introduction, Lines and Triangles Problem
Lines and Triangles: Proof by Induction
Connecting Points
Odd Points: Proof by Induction
Sums of Numbers
Bernoulli's Inequality
Coins Problem
Cutting a Triangle
Flawed Induction Proofs
Alternating Sum
Two Cells of Opposite Colors: Hints
Slides
Slides
Largest Amount that Cannot Be Paid with 5- and 7-Coins
Pay Any Large Amount with 5- and 7-Coins (Optional)
Puzzle: Hanoi Towers
Puzzle: Two Cells of Opposite Colors
Two Cells of Opposite Colors: Feedback
Puzzle: Guess a Number
Puzzle: Local Maximum (Optional)
Puzzle: Connect Points
Induction
Logic
Examples
Counterexamples
Basic Logic Constructs
If-Then Generalization, Quantification
Reductio ad Absurdum
Balls in Boxes
Numbers in Tables
Pigeonhole Principle
An (-1,0,1) Antimagic Square
Handshakes
Slides
Slides
Puzzle: Always Prime?
Examples, Counterexamples and Logic
Girls, Boys, and Two Languages
Puzzle: Balls in Boxes
Puzzle: Numbers in Boxes
Puzzle: Numbers on the Chessboard
Numbers in Boxes
How to Pick Socks
Pigeonhole Principle
Puzzle: An (-1,0,1) Antimagic Square
Invariants
Double Counting
`Homework Assignment' Problem
Invariants
More Coffee
Debugging Problem
Termination
Arthur?s Books
Even and Odd Numbers
Summing up Digits
Switching Signs
Advanced Signs Switching
Slides
Slides
Slides
Slides
Puzzle: Sums of Rows and Columns
'Homework Assignment' Problem
'Homework Assignment' Problem 2
Girls and Boys
Chess Tournaments
Coffee with Milk
More Coffee
Debugging Problem
Merging Bank Accounts
Football Fans
Puzzle: Arthur's Books
Puzzle: Piece on a Chessboard
Operations on Even and Odd Numbers
Puzzle: Summing Up Digits
Puzzle: Switching Signs
Recolouring Chessboard
Solving a 15-Puzzle
The Rules of 15-Puzzle
Permutations
Proof: The Difficult Part
Mission Impossible
Classify a Permutation as Even/Odd
Bonus Track: Fast Classification
Project: The Task
Quiz Hint: Why Every Even Permutation Is Solvable
Reading
Slides
Even permutations
Bonus Track: Finding The Sequence of Moves
Puzzle: 15
Transpositions and Permutations
Neighbor transpositions
Is a permutation even?
Bonus Track: Algorithm for 15-Puzzle
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