Enrichment • Series
AoPS Introduction to Number Theory
SL
DS
Daisy S
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.
Series Details
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.
Tutor Qualifications
- Earned A+ in AoPS Number Theory courses
- Canadian Mathematical Olympiad Qualifier and 2x AIME Qualifier
- Honor Rolls and Invitations for other math contests (such as 2021 Canadian EGMO TST)
- Create proof-based problems for a local math journal, including those related to number theory
- Feedback on Tutor Profile
✋ ATTENDANCE POLICY
It is suggested that learners attend every session as concepts will build on each other, though there is no strict attendance policy.
Dates
October 3 - March 13
Learners
69 / 75
Total Sessions
23
About the Tutor
SL
DS
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
0
Past Sessions
23
3
Oct
AM
Session 1
AoPS Math
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
8
Oct
C
Session 2
Catchup
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
10
Oct
AM
Session 3
AoPS Math
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
17
Oct
AM
Session 4
AoPS Math
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
24
Oct
AM
Session 5
AoPS Math
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)
31
Oct
AM
Session 6
AoPS Math
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.
7
Nov
AM
Session 7
AoPS Math
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
14
Nov
AM
Session 8
AoPS Math
Session Topic: Special Numbers
We will explore properties and solve fun math contest problems involving special types of numbers. The session covers:
- Factorials
- Palindromes
21
Nov
AM
Session 9
AoPS Math
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.
28
Nov
AM
Session 10
AoPS Math
Session Topic: Number Theory and Algebra
We will take a look at algebraical techniques in number theory through solving math contest problems.
5
Dec
AM
Session 11
AoPS Math
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.
12
Dec
AM
Session 12
AoPS Math
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
19
Dec
AM
Session 13
AoPS Math
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
9
Jan
AM
Session 14
AoPS Math
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
16
Jan
AM
Session 15
AoPS Math
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
23
Jan
AM
Session 16
AoPS Math
Session Topic: Office Hours & AIME Problems
We will go over learner-requested homework exercise problems. If time permits, we will cover related AIME problems.
30
Jan
AM
Session 17
AoPS Math
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
6
Feb
AM
Session 18
AoPS Math
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
13
Feb
AM
Session 19
AoPS Math
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)
20
Feb
AM
Session 20
AoPS Math
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.
27
Feb
AM
Session 21
AoPS Math
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.
6
Mar
AM
Session 22
AoPS Math
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.
13
Mar
AM
Session 23
AoPS Math
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