Introduction to Number Theory

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Introduction to Number Theory

SAT Score Range

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16 sessions

•

+47

This series ended on September 25, 2021. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

In this series, we will learn a variety of topics related to introductory number theory. In each session, we will explore concepts and apply them to practice questions, including related contest problems. You will be given lesson handouts to complement your learning and exercise/bonus problems to consolidate the knowledge. 

Please Note: having a good grasp of basic algebra, such as solving linear equations, is a prerequisite. 
*Series requested by Aisha.

Tutored by

Daisy S 🇨🇦

Certified in 21 topics

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Hi! I’m Daisy from Canada. I love to learn by helping others through peer tutoring. I’m a Canadian Mathematical Olympiad (CMO) Qualifier and a 3x AIME Qualifier. I also enjoy creating math problems for a local math journal. I have been playing the viola using the Suzuki music method since the age of 7. I attended a Montessori school from ages 3 to 12, where I benefited from an open, flexible learning environment and began helping younger classmates, following in the footsteps of the older peers who had previously helped me. I’m grateful and excited to be a tutor at schoolhouse.world!

Schedule

✋ ATTENDANCE POLICY

It’s strongly recommended to attend all sessions as concepts will build on each other and are intertwined.

SESSION 1

17

Jul

SESSION 1

AoPS Math

Sat 2:00 PM - 3:10 PM UTCJul 17, 2:00 PM - 3:10 PM UTC

Session Topic: Welcome to Number Theory!

In this session, we will go over the structure of this series and learn the basics of number theory. We will cover: 
- Intro to Numbers
- Multiples and Divisors
- Mathematical Notation
- Finding Primes

SESSION 2

22

Jul

SESSION 2

AoPS Math

Thu 2:00 PM - 3:10 PM UTCJul 22, 2:00 PM - 3:10 PM UTC

Session Topic: Prime Factorization & GCD/LCM

In this session, we will build upon our knowledge of primes and explore how we can find greatest common divisor (GCD) and lowest common multiple (LCM). We will cover: 
- Prime Factorization
- Proof By Contradiction
- GCD and Simplifying Fractions
- LCM and Common Denominator

SESSION 3

24

Jul

SESSION 3

AoPS Math

Sat 2:00 PM - 3:10 PM UTCJul 24, 2:00 PM - 3:10 PM UTC

Session Topic: Relating GCD & LCM, Euclidean Algorithm

In this session, we will continue exploring GCD/LCM and do some problem solving. We will cover: 
- GCD/LCM Relationship
- Properties of Multiples
- Euclidean Algorithm

SESSION 4

27

Jul

SESSION 4

AoPS Math

Tue 2:00 PM - 3:10 PM UTCJul 27, 2:00 PM - 3:10 PM UTC

Session Topic: Divisors and Special Numbers

In this session, we will focus on properties of divisors and look at some special numbers. We will cover: 
- The Number and Product of Divisors
- Perfect, Abundant, Deficient Numbers
- Factorials and More

SESSION 5

31

Jul

SESSION 5

AoPS Math

Sat 2:00 PM - 3:10 PM UTCJul 31, 2:00 PM - 3:10 PM UTC

Session Topic: Number Theory Problem Solving with Algebra

In this session, we will apply the concepts we have previously covered and take a look at algebraical techniques in number theory. The session consists of:
- Brief Kahoot for Review
- Problems involving both Number Theory and Algebra

SESSION 6

2

Aug

SESSION 6

Office Hours

Mon 1:30 PM - 2:50 PM UTCAug 2, 1:30 PM - 2:50 PM UTC

In this optional session, we will go over learner-requested homework exercise problems from Sessions 1 - 5, inclusive. 

SESSION 7

3

Aug

SESSION 7

AoPS Math

Tue 2:00 PM - 3:10 PM UTCAug 3, 2:00 PM - 3:10 PM UTC

Session Topic: Bases Part I - Base Number Systems

This session is an introduction to number bases and their relationships to each other. It covers:
- Base Number Systems & Expanded Form (including Base 10)
- Base Number Conversions
- Base Number Problems

SESSION 8

6

Aug

SESSION 8

Catchup

Fri 2:00 PM - 3:20 PM UTCAug 6, 2:00 PM - 3:20 PM UTC

Topic: Bases Part I - Base Number Systems  (Session 7 Review)

This optional session is for anyone who was unable to come to Session 7 or who would like to review the Session 7 bases content in preparation for our upcoming “Bases Part II - Base Number Arithmetic” session.  

SESSION 9

7

Aug

SESSION 9

AoPS Math

Sat 2:00 PM - 3:20 PM UTCAug 7, 2:00 PM - 3:20 PM UTC

Session Topic: Bases Part II - Base Number Arithmetic

This session is a continuation of our exploration on bases introduced in Session 7. It covers:
- Base Number Arithmetic (including Divisibility)
- Clever Base Number Problems

SESSION 10

14

Aug

SESSION 10

AoPS Math

Sat 2:00 PM - 3:30 PM UTCAug 14, 2:00 PM - 3:30 PM UTC

Session Topic: Introduction to Modular Arithmetic

This session is an introduction to mods, which uses remainders to discover certain properties, such as divisibility. We will look at:
- Congruence & Residues
- Addition, Subtraction, and Multiplication with Congruences
- Modular Arithmetic Problems

SESSION 11

21

Aug

SESSION 11

AoPS Math

Sat 2:00 PM - 3:30 PM UTCAug 21, 2:00 PM - 3:30 PM UTC

Session Topic: Modular Multiplication & Office Hours (Exercise Problem Session)

This session consists of two parts. In the first part, we will cover modular multiplication to lay the foundations for divisibility proofs and solving linear congruences (Sessions 12 & 13). In the second part, we will go over some learner-requested homework exercise problems from Sessions 7 - 10, inclusive. If time permits, we’ll cover the AIME problems from the Base Number Arithmetic session.

SESSION 12

28

Aug

SESSION 12

AoPS Math

Sat 2:00 PM - 3:30 PM UTCAug 28, 2:00 PM - 3:30 PM UTC

Session Topic: Divisibility (with Modular Arithmetic)

This session will apply our introduction to modular arithmetic from Session 10 to divisibility. It covers:
- Modular Exponentiation
- Divisibility Rules & Proofs
- Divisibility Problem Solving

SESSION 13

4

Sep

SESSION 13

AoPS Math

Sat 2:00 PM - 3:30 PM UTCSep 4, 2:00 PM - 3:30 PM UTC

Session Topic: Linear Congruences

In this session, we will take a look at linear congruences and how to solve them. It covers:
- Intro to Linear Congruences
- Modular Inverses
- Solving Linear Congruences (including Systems)

SESSION 14

11

Sep

SESSION 14

AoPS Math

Sat 2:00 PM - 3:20 PM UTCSep 11, 2:00 PM - 3:20 PM UTC

Session Topic: Linear Congruences Continued and Office Hours

In this optional session, we will extend our knowledge on solving linear congruences. We will take a look at:
- Modular Inverses & Euclidean Algorithm
- System of 3 Congruences
- Related Practice Problems (AMC & AIME)
Then, we will go over learner-requested homework problems from Sessions 12 and 13.

SESSION 15

18

Sep

SESSION 15

AoPS Math

Sat 2:00 PM - 3:20 PM UTCSep 18, 2:00 PM - 3:20 PM UTC

Session Topic: Number Sense

In this session, we will explore efficient number theory problem solving techniques through AMC 8, AMC 10, AMC 12, and AIME Problems.

SESSION 16

25

Sep

SESSION 16

AoPS Math

Sat 2:00 PM - 3:20 PM UTCSep 25, 2:00 PM - 3:20 PM UTC

Session Topic: Number Theory Contest Problem Solving

In this session, we will apply what we have learned in this series to AMC 8, AMC 10, AMC 12, and AIME Problems.

Public Discussion

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Jul 17 - Sep 25

11 weeks

70 - 90 mins

/ session

SCHEDULE

Saturdays

2:00PM