#### LIVE 25: Introduction

Tu/W/Th/F/M 1:45–2:45pm from 7/12 (Your Time*)

This LIVE course contains a total of 20 hours of live video instruction (~$22/hour), plus 1 year of access to Prof. Loh's recorded videos from this course.

We’ve carefully designed our courses to maximize engagement. Each of our LIVE classrooms has at least one staff member for every 13 students. The typical class size is around 30 students.

* The official meeting time for this course is 9:45am in New York.

Diagnostic Tests:

### 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 homework challenge

### 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

**ANGELA CAI**

UPenn Class of 2026 • Co-President of INTEGIRLS-NYC chapter • MPFG qualifier • Self-taught competitive math

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