AoPS Introduction to Number Theory

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AoPS Introduction to Number Theory

SAT Score Range

•

23 sessions

•

+66

This series ended on March 13, 2022. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

In this series, we will explore a variety of introductory number theory topics. In each session, we will cover concepts and apply them to practice problems, including those from AMC and AIME. You will be given session slides and homework, in the form of review and challenge problems, to help you further consolidate the knowledge. 

The content and pacing of this series have been revised and refined based on previous learners’ feedback and the corresponding experience the tutor has gained from the summer series. In addition, its session start time and duration have been adjusted to take into account the school year.

Please Note: Having a good grasp of basic algebra techniques, such as solving linear equations and inequalities, is a prerequisite.
*Series requested by Angelina, et al.

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 is suggested that learners attend every session as concepts will build on each other, though there is no strict attendance policy.

SESSION 1

3

Oct

SESSION 1

AoPS Math

Sun 1:00 AM - 2:10 AM UTCOct 3, 1:00 AM - 2:10 AM UTC

Session Topic: Welcome to Number Theory! 
We will go over the different aspects of this series and gain a deeper understanding of the world of numbers. We will cover:
- The Hierarchy of Numbers
- Relationship between Mathematical Operations and Number Theory 
- Mathematical Notation

SESSION 2

8

Oct

SESSION 2

Catchup

Fri 11:00 PM - Sat, 12:10 AM UTCOct 8, 11:00 PM - Oct 9, 12:10 AM UTC

This optional requested session is for anyone who was unable to attend or who would like to review Session 1.
We will cover:
- An Overview of the Series
- The Hierarchy of Numbers
- Relationship between Mathematical Operations and Number Theory
- Mathematical Notation

SESSION 3

10

Oct

SESSION 3

AoPS Math

Sun 1:00 AM - 2:10 AM UTCOct 10, 1:00 AM - 2:10 AM UTC

Session Topic: Parity and Primes
We will continue taking a look at how numbers can be grouped, more specifically: primes and parity. We will cover:
- Parity
- Finding Primes
- Prime Factorization and the Fundamental Theorem of Arithmetic

SESSION 4

17

Oct

SESSION 4

AoPS Math

Sun 1:00 AM - 2:20 AM UTCOct 17, 1:00 AM - 2:20 AM UTC

Session Topic: GCD/LCM
We will build upon our last session and explore how we can find greatest common divisor (GCD) and lowest common multiple (LCM). We will cover:
- Common Multiples and Divisors
- Prime Factorization & GCD/LCM
- Product Relationship between GCD and LCM

SESSION 5

24

Oct

SESSION 5

AoPS Math

Sun 1:00 AM - 2:10 AM UTCOct 24, 1:00 AM - 2:10 AM UTC

Session Topic: Euclidean Algorithm
We will explore an alternative method of finding GCD: Euclidean Algorithm. We will cover:
- Properties of Multiples under Addition and Subtraction
- Remainders & Division Theorem
- Euclidean Algorithm (including Extension)

SESSION 6

31

Oct

SESSION 6

AoPS Math

Sun 1:00 AM - 2:10 AM UTCOct 31, 1:00 AM - 2:10 AM UTC

Session Topic: Combinatorics Foundations and Office Hours
In this optional session, we will go over learner-requested homework exercise problems from Sessions 1 - 5, inclusive. Then, we will cover some combinatorics knowledge that will apply to our next sessions.

SESSION 7

7

Nov

SESSION 7

AoPS Math

Sun 1:00 AM - 2:20 AM UTCNov 7, 1:00 AM - 2:20 AM UTC

Session Topic: Divisors
We will take a deeper look at numbers that make up other numbers: divisors. We will cover:
- The Number and Product of Divisors
- The Sum of Divisors
- Perfect, Abundant, and Deficient Numbers

SESSION 8

14

Nov

SESSION 8

AoPS Math

Sun 1:00 AM - 2:30 AM UTCNov 14, 1:00 AM - 2:30 AM UTC

Session Topic: Special Numbers
We will explore properties and solve fun math contest problems involving special types of numbers. The session covers:
- Factorials
- Palindromes

SESSION 9

21

Nov

SESSION 9

AoPS Math

Sun 1:00 AM - 2:30 AM UTCNov 21, 1:00 AM - 2:30 AM UTC

Session Topic: Number Theory and Combinatorics
Oftentimes, mathematical knowledge from different branches of math is needed to solve more complex math contest problems. In this session, we will broaden the scope of our learning by solving problems that incorporate both number theory and combinatorics.

SESSION 10

28

Nov

SESSION 10

AoPS Math

Sun 1:00 AM - 2:30 AM UTCNov 28, 1:00 AM - 2:30 AM UTC

Session Topic: Number Theory and Algebra
We will take a look at algebraical techniques in number theory through solving math contest problems.

SESSION 11

5

Dec

SESSION 11

AoPS Math

Sun 1:00 AM - 2:30 AM UTCDec 5, 1:00 AM - 2:30 AM UTC

Session Topic: Algebraic Methods in Number Theory Continued & Office Hours
In this optional session, we will go over learner-requested homework exercise problems. Then, we will cover some algebraic methods of arithmetic.

SESSION 12

12

Dec

SESSION 12

AoPS Math

Sun 1:00 AM - 2:30 AM UTCDec 12, 1:00 AM - 2:30 AM UTC

Session Topic: Base Number Systems
We will take a look at number bases and their relationships to each other. The session covers:
- Base Number Systems & Expanded Form
- Base Number Conversions
- Base Number Practice Problems

SESSION 13

19

Dec

SESSION 13

AoPS Math

Sun 1:00 AM - 2:30 AM UTCDec 19, 1:00 AM - 2:30 AM UTC

Session Topic: Base Number Arithmetic
We will continue our exploration of bases introduced in the previous session. The session covers:
- Base Number Arithmetic
- Base Number Contest Problems

SESSION 14

9

Jan

SESSION 14

AoPS Math

Sun 1:00 AM - 2:30 AM UTCJan 9, 1:00 AM - 2:30 AM UTC

Session Topic: Introduction to Modular Arithmetic
We will have an introduction to mods, which uses remainders to discover certain properties of numbers, such as divisibility. The session covers:
- Congruence & Residues
- Addition, Subtraction, and Multiplication with Congruences

SESSION 15

16

Jan

SESSION 15

AoPS Math

Sun 1:00 AM - 2:30 AM UTCJan 16, 1:00 AM - 2:30 AM UTC

Session Topic: Modular Multiplication and Exponentiation
We will continue along the vein of modular arithmetic by exploring modular multiplication and exponentiation. This will lay the foundations for sessions on divisibility proofs and solving linear congruences. The session covers:
- Modular Multiplication
- Modular Exponentiation

SESSION 16

23

Jan

SESSION 16

AoPS Math

Sun 1:00 AM - 2:30 AM UTCJan 23, 1:00 AM - 2:30 AM UTC

Session Topic: Office Hours & AIME Problems
We will go over learner-requested homework exercise problems. If time permits, we will cover related AIME problems.

SESSION 17

30

Jan

SESSION 17

AoPS Math

Sun 1:00 AM - 2:30 AM UTCJan 30, 1:00 AM - 2:30 AM UTC

Session Topic: Divisibility (with Modular Arithmetic)
We will apply our modular arithmetic knowledge from previous sessions to divisibility. The session covers:
- Divisibility Rules & Proofs
- Divisibility Problem Solving

SESSION 18

6

Feb

SESSION 18

AoPS Math

Sun 1:00 AM - 2:30 AM UTCFeb 6, 1:00 AM - 2:30 AM UTC

Session Topic: Linear Congruences
We will continue expanding upon modular arithmetic by exploring linear congruences and how to solve them. The session covers:
- Intro to Linear Congruences
- Modular Inverses
- Solving Linear Congruences

SESSION 19

13

Feb

SESSION 19

AoPS Math

Sun 1:00 AM - 2:30 AM UTCFeb 13, 1:00 AM - 2:30 AM UTC

Session Topic: Systems of Linear Congruences and Related Contest Problems
We will extend our linear congruences knowledge by looking at solving systems as well as related contest problems. The session covers:
- Solving Systems of Linear Congruences 
- Linear Congruences Contest Problems (AMC/AIME)

SESSION 20

20

Feb

SESSION 20

AoPS Math

Sun 1:00 AM - 2:30 AM UTCFeb 20, 1:00 AM - 2:30 AM UTC

Session Topic: Number Sense & Office Hours
We will explore efficient number theory problem solving techniques through AMC and AIME problems. Then, we will go over learner-requested homework exercise problems from the previous sessions.

SESSION 21

27

Feb

SESSION 21

AoPS Math

Sun 1:00 AM - 2:30 AM UTCFeb 27, 1:00 AM - 2:30 AM UTC

Session Topic: Number Theory Contest Problem Solving (Part I)
In this session, we will apply what we have learned in this series to AMC and AIME Problems.

SESSION 22

6

Mar

SESSION 22

AoPS Math

Sun 1:00 AM - 2:30 AM UTCMar 6, 1:00 AM - 2:30 AM UTC

Session Topic: Number Theory Problem Solving (Part II)
In this session, we will apply our number theory knowledge and problem solving techniques to number theory contest problems.

SESSION 23

13

Mar

SESSION 23

AoPS Math

Sun 1:00 AM - 2:30 AM UTCMar 13, 1:00 AM - 2:30 AM UTC

Session Topic: Number Theory Problem Solving (Part III)
In this session, we will continue to apply our number theory knowledge and problem solving techniques to number theory contest problems

Public Discussion

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Oct 3 - Mar 13

24 weeks

70 - 90 mins

/ session

SCHEDULE

Sundays

1:00AM