Online Program Course Curriculum & Schedule
Curriculum / Course Structure

Students interested in participating in the ONLINE summer program must first be admitted through our application process. Please follow the steps as outlined on how to apply.

The deadline to apply is April 26th. Students accepted into our program will choose their desired session date(s) and courses during the open enrollment period (April 15 – May 7th).

Platform Zoom
When Session 1: June 01 – June 19
Session 2: June 22 – July 10
Session 3: July 13 – July 31

There are 15 teaching days per course, 5 times per week (Monday-Friday) and two testing days on Saturdays
Times
(all sessions)
Attention: For each session(s) you choose, you do not have to enroll in both morning and afternoon classes.
Morning Courses
8 AM PDT
(11 AM EDT / 11 PM Shanghai)
Afternoon Courses
5 PM PDT
(8 PM EDT / 8 AM Shanghai)
Algebra Algebra 1.5
Algebra 2.5
Algebra 3.5
Combinatorics Math Counts with Proofs
Counting Strategies
Combinatorial Arguments
Geometry Elements of Geometry
Computational Geometry
Geometric Proofs
Number Theory Number Sense
Modular Arithmetic
Number Theory
Download or print the course schedule.
Class Length 90-minute lecture followed by a problem session (up to 60-minutes long).
There will be a 10 minute break between lectures and problem sessions.
Class Size Maximum 25 students, Minimum 10 students (if a section fills up, we will open another section)
Tuition Cost $750 / course (for payment made on or before May 15)
$850 / course (for payment made after May 15)

Refer to our tuition/refunds page for more information
Curriculum There are four main subject areas covered in math competitions: Algebra, Combinatorics, Geometry, and Number Theory. Our goal with the Online Summer Program is to build and hone students problem solving skills in these four fields. We offer 12 courses per session which cover 3 difficulty levels in the four subjects mentioned above.

Refer to the Course Descriptions and Course Selection Tips for more information.

Course Structure The instructor(s) of each course will teach the lecture and supervise the problem sessions that follow. There will be a 10 minute break between lectures and problem sessions. Students will be split into breakout rooms with a supervising TA so they can work together; the instructor/TA will help moderate discussions and give guidance/encouragement when necessary.

Students will have several assigned homework problems which will be turned in electronically for feedback and grading. In order to achieve proficiency of the material presented in class, students are expected to work on average 1-2 hours per day for each class. If students have questions or concerns regarding the material taught, they can email the instructor/TA, participate in the problem sessions, and access the class forum. Emailed questions will be answered within 24 hours.

Because communication plays an important role in developing problem solving skills, students will be asked to participate actively in the problem sessions, i.e., to ask questions and present and defend solutions. Students can choose from one to six courses over the course of three sessions.

Program Benefits
  • Providing guidance to transition to proof based solutions
  • Making connections between topics requiring more creativity in approach
  • Developing efficiency and patience in problem solving to build success in advanced math competitions
Additional Information
  • All classes are recorded so students can revisit the material covered in class
  • We allow students to switch classes within the first two days of the online camp
  • See answers to our frequently asked questions
  • Students and parents should be familiar with our policies & expectations before enrolling
  • Students can participate in a Team Contest on Sunday August 2 (stay tuned for more details)
Suggested Resources (optional) A wide variety of books covering a large spectrum of topics and level are available. We developed a book guide to help you with the book selection based on your mathematical ability level. As a camp participant you will be able to purchase books at a significantly reduced price. More details to come!
Course Selection Tips
Course Selection Tips
  • Select the areas in which the student is most interested, or in which the student needs the most work.
  • Both the content and dificulty of each course are very important. Please read the course descriptions carefully.
  • All of our courses are challenging and beyond the scope of regular/accelerated/honor classes in school settings. There is an entry level course in each area. Each of these entry level courses will be challenging for most able young minds because these are contest mathematics courses. In particular, Algebra 1.5 is harder than any algebra course (including Algebra 1 and 2) taught in high schools, and Math Counts with Proofs is beyond the requirements for the MathCounts competitions (at state and national levels).
Course Selection Guidelines
  • If a student only has MathCounts state level experience, what courses should he/she take?
    Please choose two level 1 courses. We recommend a combination of the student’s strong subject and his/her weak subject.
  • If a student’s (9th grader or below) AMC10/12 scores are below the qualifying line for AIME, what courses should he/she take?
    Please choose two level 1 courses. We recommend a combination of the student’s strong subject and his/her weak subject.
  • If a student’s (10th grader or above) AMC10/12 scores are below the qualifying line for AIME, what course should he/she take?
    Please choose one level 1 course, with this being the student’s weak subject, and one level 2 course, with this being his/her strong subject.
  • If a student has an AIME score between 1 and 3, what courses should he/she take?
    Please choose either

    1. two level 1 courses. We recommend a combination of the student’s strong subject and his/her weak subject; OR
    2. one level 1 course, with this being the student’s weak subject, and one level 2 course, with this being his/her strong subject.
  • If a student has an AIME score between 4 and 7, what courses should he/she take?
    Please choose two level 2 courses. We recommend a combination of the student’s strong subject and his/her weak subject.
  • If a student has an AIME score between 8 and 11, what courses should he/she take?
    Please either

    1. two level 2 courses. We recommend a combination of the student’s strong subject and his/her weak subject; OR
    2. one level 2 course, with this being the student’s weak subject, and one level 3 course, with this being his/her strong subject.
  • If a student has an AIME score of 12 or above, what courses should he/she take?
    Please choose two level 3 courses. We recommend a combination of the student’s strong subject and his/her weak subject.
  • If a student’s background does not fall into any of the above, what courses should he/she take?
    Please contact AwesomeMath staff as soon as possible about the student’s background and interests, and we will make a recommendation promptly.
  • If a student’s background falls into to the above categories, but he/she wants to choose the courses not following the guidelines, what should he/she do?
    Please contact AwesomeMath staff via email as soon as possible about the student’s background and interests, and we will make a recommendation promptly.

If there are still questions about our recommendation, the student might be required to take a placement test in the subjects for which he/she is not following our recommendation.

Visit the course descriptions page for a list of courses and sample problems.

Course Descriptions
Subject Beginning
(Level 1)
Courses
Intermediate
(Level 2)
Courses
Advanced
(Level 3)
Courses
Algebra Algebra 1.5 Algebra 2.5 Algebra 3.5
Combinatorics Math Counts with Proofs Counting Strategies Combinatorial Argument
Geometry Elements of Geometry Computational Geometry Geometry Proofs
Number Theory Number Sense Modular Arithmetic Number Theory
These courses are computationally oriented with a touch on proofs. They are suited for most USA math competitions (MathCounts National level, AMC10, AMC12, ARML, and the entry level of AIME). These courses are about half computational problems and half proofs. They are well suited for the hard end of AIME and the entry level of Math Olympiad contests. These courses are proof oriented. They are well suited for students who can easily pass AIME and are seriously preparing for Math Olympiad contests.
Algebra Courses
  • Algebra 1.5
    Develops essential skills such as factoring, grouping, recognizing roots, telescoping sums/products, and rationalizing. Solving (systems of) equations/inequalities (linear, absolute value, quadratic, rational, radical) is the main theme of the course. Discriminants, Viete’s relations, and symmetric polynomials also play a central role. This is the entry level algebra course. It covers all AMC levels and easy end of AIME and ARML. This course is a good fit for students with MathCounts state level experience, AMC10/12 scores approaching AIME qualifying cuts, or an AIME score between 1 and 3.
  • Algebra 2.5
    Studies special systems of equations, discriminants, Viete’s relations, symmetric polynomials, functional properties. Introduces (weighted) AM–GM–HM and Cauchy–Schwarz inequalities. This is the intermediate level algebra course. It covers the hard end of AMC12, and the medium to hard end of ARML and AIME. A student with an AIME score between 4 and 7 should be a good fit for this course.
  • Algebra 3.5
    Discusses functional equations, classical inequalities such as AM-GM-HM, Cauchy-Schwarz, Power-mean, and Jensen’s inequalities, as well as Muirhead’s and Schur’s inequalities, and inequalities related to symmetric polynomials. This is the advanced level algebra course. It covers the hard end of AIME and all levels of USAMO. A student with a strong algebra background and an AIME score of 8 or above should consider this course.
Combinatorics Courses
  • Math Counts with Proofs
    Studies the addition and multiplication principles, permutations and combinations, and probability. Teaches how to deal with over-counting and many useful properties of integer divisors. It also introduces mathematical proofs using pigeonhole principle, well-ordering, etc. This is the entry level combinatorics course. It covers MathCounts, all the AMC levels, and the easy end of AIME and ARML. This course is a good fit for students with MathCounts state level experience, AMC10/12 scores approaching AIME qualifying cuts, or AIME scores between 1 and 3.
  • Counting Strategies
    Discusses counting strategies such as the addition and multiplication principles, permutations and combinations, properties of the binomial coefficients, bijections, recursions, and the inclusion- exclusion principle. This is the intermediate level combinatorics course. It covers the hard end of AMC12, the medium to hard end of AIME and ARML, as well as the beginning USAMO level. A student with an AIME score between 4 and 7 should be a good fit for this course.
  • Combinatorial Arguments
    Introduces methods of mathematical proofs, including induction, proofs by contradiction, the Pigeonhole Principle, the well-ordering principle, colorings, assigning weights, bijections/mappings, recursion, calculating in two ways, and combinatorial constructions. Topics may include graph theory and combinatorial geometry. A focal point of the course is combinatorial number theory. This is the advanced level combinatorics course. It covers the hard end of AIME and the medium to hard end of USAMO. A student who is familiar with mathematics proofs and has an AIME score of 8 or above should consider this course.
Geometry Courses
  • Elements of Geometry
    Deals with computational geometry in two dimensions using Euclidean methods, including manipulation of angles and lengths, as well as the basic properties of polygons, circles, and the relations between figures. Analytic geometry is also a focal point. This is the entry level geometry course. It covers MathCounts, all AMC levels, and the easy end of AIME and ARML. This course is a good fit for students with MathCounts state level experience, AMC10/12 scores approaching AIME qualifying cuts, or AIME scores between 1 and 3.
  • Computational Geometry
    Studies non-synthetic techniques in solving geometry problems: coordinate geometry, vectors (2- and 3- dimensional), planes, spheres, trigonometry, and complex numbers. Features many important geometric themes: The Law of Sines and the Law of Cosines, Ptolemys theorem, Cevas theorem, Menelauss theorem, Stewarts theorem, Herons and Brahmaguptas formulas, Brocard points, dot product and the vector form of the Law of Cosines, the Cauchy-Schwarz inequality, 3-dimensional coordinate systems, as well as linear representation and traveling on the earth (sphere). This is the intermediate level geometry course. It covers the hard end of AMC12, the medium to hard end of AIME and ARML. A student with an AIME score between 4 and 7 should consider this course.
  • Geometric Proofs
    Focuses on classical topics such as concurrency, col-linearity, cyclic quadrilaterals, special centers/points of triangles, and geometric constructions. Introduces important transformations translation, reflections, and spiral similarities, with a touch on projective and inversive geometry. This is the advanced level geometry course. It covers the hard end of AIME and the medium to hard end of USAMO. A student with a strong background in geometry and an AIME score of 8 or above should consider this course.
Number Theory Courses
  • Number Sense
    Studies divisibility, factoring, numerical systems, divisors and arithmetic functions of divisors. Setting-up and solving linear Diophantine equations is also a focal point of the course. This is the entry level number theory course. It covers MathCounts, all AMC levels, and the easy end of AIME and ARML. This course is a good fit for students with MathCounts state level experience, AMC10/12 scores approaching AIME qualifying cuts, or AIME scores between 1 and 3.
  • Modular Arithmetic
    Develops essential skills in number theory: divisibility, the division algorithm, prime numbers, the Fun- damental Theorem of Arithmetic, GCD, LCM, Bezouts identity, the Euclidean algorithm, modular arithmetic, and divisibility criteria in the decimal system. Studies numerical functions such as the number of divisors or the sum of divisors of integers. This is the intermediate level number theory course. It covers the hard end of AMC12 and the medium to hard end of AIME and ARML. A student qualified for AIME with a score between 4 and 7 should be a good fit for this course.
  • Number Theory
    Focuses on in-depth discussions of Diophantine equations, residue classes, quadratic reciprocity, Fermats little theorem, Eulers theorem, primitive roots, and Eulers totient function, etc. This is the advanced level number theory course. It covers the hard end of AIME and the medium to hard end of USAMO. A student with a strong background in number theory and an AIME score of 8 or above should consider this course.

Download sample problems. Check out course selection tips.