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Enrichment • Series

Introduction to Number Theory

Daisy S

Series Details

Sessions

Public Discussion

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.

Series Details

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.

Tutor Qualifications

- Earned an A+ in the AoPS Introduction to Number Theory course

- Canadian Mathematical Olympiad Qualifier

- 2x AIME Qualifier

- Honor Rolls and Invitations for other math contests (such as 2021 Canadian EGMO TST)

- Learners' Feedback on SHW Tutor Profile

✋ ATTENDANCE POLICY

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

Dates

July 17 - September 25

Learners

50 / 50

Total Sessions

About the Tutor

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!

View Daisy S's Profile

Upcoming Sessions

Past Sessions

Jul

Session 1

AoPS Math

Sat Jul 17, 2021, 2:00 PM

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

Jul

Session 2

AoPS Math

Thu Jul 22, 2021, 2:00 PM

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

Jul

Session 3

AoPS Math

Sat Jul 24, 2021, 2:00 PM

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

Jul

Session 4

AoPS Math

Tue Jul 27, 2021, 2:00 PM

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

Jul

Session 5

AoPS Math

Sat Jul 31, 2021, 2:00 PM

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

Aug

Session 6

Office Hours

Mon Aug 2, 2021, 1:30 PM

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

Aug

Session 7

AoPS Math

Tue Aug 3, 2021, 2:00 PM

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

Aug

Session 8

Catchup

Fri Aug 6, 2021, 2:00 PM

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.  

Aug

Session 9

AoPS Math

Sat Aug 7, 2021, 2:00 PM

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

Aug

Session 10

AoPS Math

Sat Aug 14, 2021, 2:00 PM

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

Aug

Session 11

AoPS Math

Sat Aug 21, 2021, 2:00 PM

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.

Aug

Session 12

AoPS Math

Sat Aug 28, 2021, 2:00 PM

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

Sep

Session 13

AoPS Math

Sat Sep 4, 2021, 2:00 PM

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)

Sep

Session 14

AoPS Math

Sat Sep 11, 2021, 2:00 PM

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.

Sep

Session 15

AoPS Math

Sat Sep 18, 2021, 2:00 PM

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.

Sep

Session 16

AoPS Math

Sat Sep 25, 2021, 2:00 PM

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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