Enrichment • Series
Beginner's Guide to Problem Solving
PL
SS
Shadman S
This series ended on November 4, 2022. All 1:1 and group chats related to this series are disabled 7 days after the last session.
Series Details
About
This is a course that will go over all the basic must-knows to be proficient in problem-solving (competitive math), starting from square 1! Optional Prerequisites - Geometry, Algebra, and Right Triangle Trigonometry. Anyone can join even if they don't know the prerequisites - though their understanding of the super rigorous proofs will be slightly impaired. Goal is to prepare learners for AMC 10 - level math: particularly to get qualifying scores for AIME.
Tutor Qualifications
I am an experienced mathematics problem solver. Along with other qualifications, I have:
- qualified for AIME twice, both on the 10 and the 12.
- received a 4 and a 9 on the respective AIMES
- participated in ARML, BMT, and HMMT.
Link to the syllabus (and other important links) here:
https://docs.google.com/document/d/15G9lcXuEjSewLML2IljF2wV5nU18x1dHEIueC81PP44/edit?usp=sharing
✋ ATTENDANCE POLICY
This series is incredibly dense and full of novel mathematics - missing a session would undoubtedly put a learner at a disadvantage. Makeup sessions will be available though - and please do not miss too many sessions without giving me prior notice or else I will be forced to withdraw you.
Dates
June 11 - November 4
Learners
77 / 100
Total Sessions
57
About the Tutor
PL
SS
Hey there! I'm a current undergraduate freshman at Stony Brook University, and I love the STEM fields most out of all my subjects in school! With that being said, though I tutor mostly competitive math nowadays, I also tutor high school math and science. I also join many sessions on Schoolhouse, because there are so many things to learn and enjoy in Schoolhouse - though I haven't joined many series recently, I had a lot of fun in Taeho's Korean Camp last summer! Outside of Schoolhouse, I love to play basketball and Pokemon.
View Shadman S's Profile
Upcoming Sessions
0
Past Sessions
57
11
Jun
O
Session 1
Orientation
We get to know each other, and the syllabus I have prepared for the series! No problem if you miss this session in particular - though attendance would be highly appreciated! Will also introduce AoPS resources - in particular past exams + Alcumus!
12
Jun
AM
Session 2
AoPS Math
Will go over basic geometry for triangles - congruence criterion, bh/2 area formula, types of triangles, and mention linear pairs and . Will introduce triangle theorems peripherally - only plan to go over three main ones: Triangle Angle Sum Theorem, Similar Triangles, and the Pythagorean theorem. Proofs!!!!
18
Jun
AM
Session 3
AoPS Math
Practice problems from the last set. Will be focused mainly on angle chasing + use of the Pythagorean Theorem! The proof of the basic tenets of trigonometry will follow the problem solving!!
19
Jun
AM
Session 4
AoPS Math
I will first explain what circles, perpendicular bisectors, and angle bisectors represent as sets of points. Then, I will go over basic tenets of trigonometry! I expect that this in itself should take a while to explain well, so I can't guarantee problem sets for after session work!
25
Jun
R
Session 5
Review
We will review everything we have learned in the last three sessions! There will be a massive Kahoot in the end of this!!!
26
Jun
AM
Session 6
AoPS Math
Review #2 - we will try to review the topics we learnt so far just like the last session!
28
Jun
AM
Session 7
AoPS Math
Beginning of summer, so this session is on a Monday! First, we talk about circles, angle bisectors, and perpendicular bisectors. We talk about area of triangles more officially - will introduce 1/2 ab sin C (partner-in-crime with TART). Then, we will review some problems involving TART, similar triangles, and 1/2(ab)sin C especially! Towards the end, we will introduce the idea of the circumradius and inradius: important for the next lesson's area formulas! I will sadly not prove the existences of the incenter and circumcenter: for now, people will have to take it for granted. :(
29
Jun
AM
Session 8
AoPS Math
This lesson will cover first the rs (inradius) area formula, and then we will formally prove extended law of sines. This should take up the entire session: I will prove abc/4R (circumradius) by the end of the session, but in case people need me to slow down for the circle geometry, I will spend this entire session being as slow as people need me to be.
1
Jul
AM
Session 9
AoPS Math
First, we need to talk circles for a bit, but then we can prove the extended law of sines and the circumradius area formula, after which we will practice all the area formulas we learned so far. For the second half, rapid proof of both the existence of the circumcenter and the incenter will occur, because up next comes something shocking.
2
Jul
OH
Session 10
Office Hours
Our first office hours! Come if you have any questions/concerns!
3
Jul
OH
Session 11
Office Hours
Office hours! Come if you have any questions/concerns! (Try to fill out this form before you come though: https://forms.gle/HgX3hVkdTes2pYAWA)
5
Jul
AM
Session 12
AoPS Math
Happy Independence Day in the US!!! I'm moving this to a Tuesday to let people enjoy the 4th :). Today, I will prove Heron's formula algebraically. This may take the entire session up, but if it doesn't, we will practice Heron questions.
6
Jul
AM
Session 13
AoPS Math
We will officially start this session with a problem set of triangle area problems!! The remainder of the session is to introduce the next topic: quadrilaterals!!!
8
Jul
AM
Session 14
AoPS Math
We will start with the properties of parallel lines : a little important to understand for quadrilaterals, but even more so in the future. Afterwards, parallelograms - the very first kinds of quadrilaterals normally studied in HS geometry!
9
Jul
OH
Session 15
Office Hours
Office hours! Come if you have any questions/concerns!
12
Jul
AM
Session 16
AoPS Math
We will talk about more properties of parallelograms - specifically about angles, side lengths, diagonals, area - and special kinds of parallelograms, such as rhombi and rectangles! Proofs everywhere!
13
Jul
AM
Session 17
AoPS Math
Recognizing a growing need of the system (which will definitely be apparent by now), I introduce coordinate geometry! Basics here, more important things in the next session! Practice problems galore!
15
Jul
AM
Session 18
AoPS Math
We will continue coordinate geometry - now we talk about slopes, perpendicular & parallel lines, and line equations! Practice problems galore!
16
Jul
OH
Session 19
Office Hours
Office hours! Come if you have any questions/concerns!
18
Jul
AM
Session 20
AoPS Math
We will slowly ease our way back to quadrilaterals, starting with trapezoids! I'll talk about the special properties of trapezoids. It should not take very long, so we will also have practice problems.
20
Jul
AM
Session 21
AoPS Math
Law of cosines proof! Incredibly important as we delve into quads!
22
Jul
AM
Session 22
AoPS Math
Now, we can talk about cyclic quads! Just an intro this time around and really only the basics - how to identify cyclics, what cool properties they have, etc.
23
Jul
OH
Session 23
Office Hours
Office hours! Come if you have any questions/concerns!
25
Jul
R
Session 24
Review
Today we are going to review everything we have done so far! There will a problem set that we can go over, and people can ask me anything they want about competition math, because we are very close to finishing off our geometry section of this class!
27
Jul
AM
Session 25
AoPS Math
We are going to go over some important facts about the circle! We have already talked about inscribed angles, but there are also different kinds of angles and powers of points galore! Practice problems will be available!
29
Jul
AM
Session 26
AoPS Math
Now we can talk about Ptolemy's! We will first go over the previous day's lesson, then we will prove Ptolemy's in a modern way that also gives us an important inequality!!
30
Jul
OH
Session 27
Office Hours
Office hours! Come if you have any questions/concerns!
8
Aug
AM
Session 28
AoPS Math
It's been a while, so instead of really trying to do anything new, I want to try just doing some problems. We'll even do some AMC 10 geo together!
10
Aug
AM
Session 29
AoPS Math
We will review Ptolemy's theorem for people first, then we can set about using triangles to prove Bretschneider's, which is two parts. Today is part one!
12
Aug
AM
Session 30
AoPS Math
We will review Ptolemy's theorem for people first, then we can set about using triangles to prove Bretschneider's, which is two parts. Today is part one!
13
Aug
OH
Session 31
Office Hours
Office hours! Come if you have any questions/concerns!
14
Aug
OH
Session 32
Office Hours
Office hours! Come if you have any questions/concerns!
15
Aug
AM
Session 33
AoPS Math
Now we can finally prove Bretschneider's! We will talk about the special Brahmagupta case, and there should even be a problem set to help!!
17
Aug
R
Session 34
Review
At last, I think we have covered pretty much all the competition geometry that we need (and often trips people up)! Today I'm ready to take any question about the past units, and a special problem set will be up by August 19th! The next couple of sessions will cover AMC geometry. problems in the flesh!
19
Aug
R
Session 35
Review
First day of AMC problems! We are going to start with a normal AMC: I haven't yet taught number theory, but I want to see how it goes :)
20
Aug
OH
Session 36
Office Hours
Office hours! Come if you have any questions/concerns!
26
Aug
R
Session 37
Review
First day! Some questions will not be geo, but I'll be on AMC 8 - should be simple enough! We'll do a full AMC 8 - aiming to get everyone to try each question and answer :)
27
Aug
OH
Session 38
Office Hours
Office hours! Ask any questions you need or come to catch up!
31
Aug
R
Session 39
Review
More review! After today we'll start AMC questions!
2
Sep
R
Session 40
Review
More review! After today we'll start AMC questions!
3
Sep
OH
Session 41
Office Hours
Office hours! Come if you have any questions or need to catch up!
7
Sep
R
Session 42
Review
At last, I think we have covered pretty much all the competition geometry that we need (and often trips people up)! Today I'm ready to take any question about the past units, and a special problem set will be up by Sep 6th!
11
Sep
R
Session 43
Review
We'll keep doing the AMC 10 from the last session!
12
Sep
R
Session 44
Review
We'll keep doing the AMC 10 from the last session!
18
Sep
AM
Session 45
AoPS Math
This is the beginning of our algebra unit! We will start with basic understanding of polynomials and their roots, with special emphasis on 2nd degree and lower polynomials. Theorems to go over: Fundamental Theorem of Algebra
19
Sep
AM
Session 46
AoPS Math
Today we will learn about factored form in algebra! We will go over how to factor by grouping today, but we will also attempt to explain factoring by adding/subtracting a constant (example completing the square). Quadratic formula proof!
26
Sep
AM
Session 47
AoPS Math
Now we will go over Vieta's formulas for polynomials! We'll prove it using factored form, then do some problems!
27
Sep
AM
Session 48
AoPS Math
Now we will go over Vieta's formulas for polynomials! We'll prove it using factored form, then do some problems!
28
Sep
R
Session 49
Review
We'll review everything we've learnt so far with a mandatory problem set! Whatever we don't do today will be homework due next week.
2
Oct
AM
Session 50
AoPS Math
We are going to talk about transformations today! Today we will devote graphical time to explaining rotations, reflections, and translations.
3
Oct
AM
Session 51
AoPS Math
Vieta's Alcumus crash course! Today, I'm going to need everyone to be involved :)
9
Oct
AM
Session 52
AoPS Math
Today we have to start number theory! Topics include: greatest common divisor, least common multiple, modular algebra, and more!
10
Oct
AM
Session 53
AoPS Math
Continuing number theory: we'll talk about more factoring problems, Diophantine equations, and some important theorems involving modular algebra and combinations!
17
Oct
AM
Session 54
AoPS Math
We will be starting combinatorics! We'll rush through basic combinatoric arguments, set theory, permutations vs combinations, and basic level problems!
23
Oct
AM
Session 55
AoPS Math
More review of combinatorics, and we will add in stars and bars and bridge-walking! More Alcumus problems!
3
Nov
AM
Session 56
AoPS Math
Mock AMC A!
4
Nov
AM
Session 57
AoPS Math
Mock AMC B!