Euclidiad Level 1 (Junior) Short Course in Combinatorics and Geometry
A very basic course on elementary counting oriented towards entry level olympiads such as AMC8/10, SASMO/SEAMO and junior level MOMC. This course covers standard material in elementary counting such as multiplication and addition principles in counting, permutations and combinations considered with or without repetitions. However, the problems are oriented more towards problem-solving rather than high school material.
Combinatorics: Lecture Slides and Videos
- Lesson 1 - Basic Counting Principles: slides pdf
- Video 1 - Lesson 1 on Steroids: slides pdf, video link
- Lesson 2 - Permutations and Factorials: slides pdf
- Video 2 - Fun Puzzles in Combinatorics: slides pdf, video link
- Lesson 3 - Combinations: slides pdf
- Video 3 - Overcounting and Circular Permutations: slides pdf, video link
- Lesson 4 - Permutations with Repetitions: slides pdf
- Video 4 - Stars and Bars Trick, Combinatorial Identities: slides pdf, video link
- Lesson 5 - Probability: slides pdf
- Video 5 - Review: slides pdf, video link
Combinatorics: Assignments
- Homework 1: form link
- Homework 2: form link
- Homework 3: form link
- Homework 4: form link
- Homework 5: form link
Geometry: Lecture Slides and Videos
- Lesson 1 - Areas and Ratios: slides pdf
- Video 1 - Extra Problems on Areas: slides pdf, video link
- Lesson 2 - Angles in Lines and Polygons: slides pdf
- Video 2 - Extra Problems on Angles: slides pdf, video link
- Lesson 3 - Right Triangles: slides pdf
- Video 3 - More on Right Triangles: slides pdf, video link
- Lesson 4 - Ratios and Similarity: slides pdf
- Lesson 5 - Triangle Congruence: slides pdf