Basic Algebra
Variables, solving equations, substitution, inequalities, and when the inequality sign flips. The language of algorithms.
Lessons
1. Intro
The Goal
2. What is a Variable?
Representing unknowns
3. Vocabulary - Expression
Combination of numbers and variables
4. Vocabulary - Equation
Statement of equality
5. Balancing Equations
The golden rule
6. Solving Linear Equations
Isolating the variable
7. Quiz: Solving Equations
Knowledge check
8. Substitution
Replacing variables with values
9. Combining Like Terms
Simplifying expressions
10. The Distributive Property
Expanding expressions
11. Factoring Basics
Reverse of distribution
12. Quiz: Simplification
Knowledge check
13. Inequalities
Greater than and less than
14. Why Flip the Sign?
Negative multiplication rule
15. The Quadratic Formula
Solving quadratic equations
16. Vocabulary - Discriminant
Determining solution count
17. Systems of Equations
Multiple equations together
18. Solving by Substitution
Replace one variable
19. Solving by Elimination
Adding or subtracting equations
20. Quiz: Systems of Equations
Knowledge check
21. Problem - Two Sum
LeetCode 1
22. Two Sum - The Equation
What you're solving
23. Two Sum - Hash Map Approach
Efficient lookup
24. Two Sum - Implementation
In pseudocode
25. Lessons from Two Sum
summary
26. Problem - Valid Perfect Square
LeetCode 367
27. Valid Perfect Square - The Equation
What you're checking
28. Valid Perfect Square - Binary Search
Narrowing the range
29. Valid Perfect Square - Implementation
In pseudocode
30. Lessons from Valid Perfect Square
summary
31. Problem - Container With Most Water
LeetCode 11
32. Container - The Formula
Maximizing area
33. Container - Two Pointer Strategy
Greedy approach
34. Container - Why Two Pointers Work
Proof sketch
35. Container - Implementation
In pseudocode
36. Lessons from Container
summary
37. Algebra in Complexity Analysis
Simplifying runtime formulas
38. Recurrence Relations
Recursive algorithm analysis
39. Isolating Variables in Loops
Finding loop bounds
40. Quiz: Complexity Analysis
Knowledge check
41. Manipulating Inequalities
Proving bounds
42. Common Algebraic Patterns in CP
Formulas you'll see often
43. Practice - Missing Number
LeetCode 268
44. Practice - Sqrt(x)
LeetCode 69
45. Practice - Maximum Subarray
LeetCode 53
46. Section Recap
What we learned