#### LIVE 27: Introduction

Tu/W/Th/F/M 1–2pm from 7/12 (USA Eastern Time)

This LIVE course contains a total of 20 hours of live video instruction (~$20/hour), plus 1 year of access to Prof. Loh's recorded videos from this course.

### Calendar

Classes will meet on the highlighted dates. Click on any date to view the topics for that day.

Color Key:

Lesson on new topic

Discuss exam assigned for homework

### Syllabus

The 20 course meetings are split in 16 lessons (called Day 1 through Day 16 below), and 4 homework exam discussions. Each exam discussion meeting happens after 4 lessons.

**Day 1**

Geometry: areas of plane figures; congruent triangles; Pythagorean Theorem

**Day 2**

Algebra; Geometry; Number Theory: area and volume of 3-D solids; prime numbers; prime factorization; systems of equations; transforming equations; square roots

**Day 3**

Combinatorics: permutations; exclusion; complementary counting

**Day 4**

Probability: counting; permutations; symmetry

**Day 5**

Logic; Algebra; Statistics: equations in one variable; arithmetic series; the substitution method; average; word problems

**Day 6**

Geometry: volume; similar figures; ratio and proportion; proportional lengths

**Day 7**

Number Theory: least common multiple; prime numbers; unique factorization

**Day 8**

Combinatorics: combinations; binomial coefficient identities; the multiplication principle

**Day 9**

Algebra: rate-time-distance problems; problem-solving using diagrams

**Day 10**

Geometry: circumference of a circle; irrational numbers; the distributive property; using equations to solve problems

**Day 11**

Probability: percents with applications; decimals; conditional probability; sets; total probability; equations in one variable

**Day 12**

Number Theory: word problems; parity; number of factors; prime factorization

**Day 13**

Geometry: angles of a polygon; sum of angles of a polygon; properties of parallel lines; interior and exterior angles;

**Day 14**

Algebra: reciprocals; sequences and series; factoring integers; least common denominator

**Day 15**

Combinatorics: counting; permutations; problem-solving using diagrams; linear recurrence relations; Fibonacci sequences

**Day 16**

Number Theory: Integers modulo m; square numbers; number sense techniques; variables

### Co-Stars

**ERIC ZHAN**

National MATHCOUNTS competitor for Washington • 2022 USAJMO winner • Likes to swim

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**MICHAEL BUDD**

National MATHCOUNTS competitor for Illinois • 3-time AIME qualifier • Plays piano & basketball • Member of his HS student government

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