## Preparing for College Mathematics

Entering a college-level math course can be a difficult transition— high school math has laid a foundation, but college math re-emphasizes proofs, which many students haven’t touched since geometry. This course will prepare math-minded students for this higher level!

Locations: Palo Alto

Cost: \$110/hr.

Recommended hours: 8-12

Goals:

• Construct sound college-level proofs
• Learn derivations and proofs of important fundamental math theorems

## Course Description:

A negative times a negative is positive. a^2 + b^2 = c^2. The quadratic formula. If the sum of digits in a number is a multiple of three then that number is divisible by 3. Throughout their mathematical education, students learn many formulas, rules, theorems, and techniques that they apply to solve problems. However, few courses devote time to demonstrating how and why these rules work. College level math courses begin to emphasize understanding the “why” and require students to prove the validity of rules– a task for which students often find themselves unprepared.

This course will expose students to proof techniques and more abstract mathematical thinking by examining major results from their coursework and proving their validity. It is geared towards students who are considering pursuing mathematics as a major in college. Students who have completed precalculus or higher will get the most out of the course, but it will be tailored to the level of any student.

## Preparing for College Mathematics Topics:

We will select and teach the topics that will best match your student’s level and interest and build a personally tailored curriculum from these sample lessons.

#### Logic

Review if/then statements and other tools for constructing valid arguments

#### Proof-writing

Deductive and inductive reasoning, direct and indirect proofs

#### Selected Proof Topics

Pythagorean theorem, triangle sum theorem, financial math (investments), number theory

## Make the Most of the Summer!

Students who stay actively engaged in the learning process during the summer perform better during the school year.

Peninsula Main Phone Number (650) 331-3251 