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Beginner's Guide to Problem Solving

SAT Score Range

•

57 sessions

•

+74

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.

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.

Tutored by

Shadman S 🇺🇸

Certified in 106 topics

View Profile

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.

Schedule

✋ 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.

SESSION 1

11

Jun

SESSION 1

Orientation

Orientation

Sat 11:00 PM - Sun, 12:30 AM UTCJun 11, 11:00 PM - Jun 12, 12:30 AM UTC

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!
SESSION 2

12

Jun

SESSION 2

AoPS Math

AoPS Math

Sun 11:00 PM - Mon, 12:30 AM UTCJun 12, 11:00 PM - Jun 13, 12:30 AM UTC

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!!!!
SESSION 3

18

Jun

SESSION 3

AoPS Math

AoPS Math

Sat 11:00 PM - Sun, 12:30 AM UTCJun 18, 11:00 PM - Jun 19, 12:30 AM UTC

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!!
SESSION 4

19

Jun

SESSION 4

AoPS Math

AoPS Math

Sun 11:00 PM - Mon, 12:30 AM UTCJun 19, 11:00 PM - Jun 20, 12:30 AM UTC

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!
SESSION 5

25

Jun

SESSION 5

Review

Review

Sat 11:00 PM - Sun, 12:30 AM UTCJun 25, 11:00 PM - Jun 26, 12:30 AM UTC

We will review everything we have learned in the last three sessions! There will be a massive Kahoot in the end of this!!!
SESSION 6

26

Jun

SESSION 6

AoPS Math

AoPS Math

Sun 11:00 PM - Mon, 12:30 AM UTCJun 26, 11:00 PM - Jun 27, 12:30 AM UTC

Review #2 - we will try to review the topics we learnt so far just like the last session!
SESSION 7

28

Jun

SESSION 7

AoPS Math

AoPS Math

Tue 11:00 PM - Wed, 12:30 AM UTCJun 28, 11:00 PM - Jun 29, 12:30 AM UTC

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. :(
SESSION 8

29

Jun

SESSION 8

AoPS Math

AoPS Math

Wed 11:00 PM - Thu, 12:30 AM UTCJun 29, 11:00 PM - Jun 30, 12:30 AM UTC

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.
SESSION 9

1

Jul

SESSION 9

AoPS Math

AoPS Math

Fri 11:00 PM - Sat, 12:30 AM UTCJul 1, 11:00 PM - Jul 2, 12:30 AM UTC

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.
SESSION 10

2

Jul

SESSION 10

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCJul 2, 11:00 PM - 11:40 PM UTC

Our first office hours! Come if you have any questions/concerns!
SESSION 11

3

Jul

SESSION 11

Office Hours

Office Hours

Sun 11:00 PM - 11:40 PM UTCJul 3, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns! (Try to fill out this form before you come though: https://forms.gle/HgX3hVkdTes2pYAWA)
SESSION 12

5

Jul

SESSION 12

AoPS Math

AoPS Math

Tue 11:15 PM - Wed, 12:45 AM UTCJul 5, 11:15 PM - Jul 6, 12:45 AM UTC

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.
SESSION 13

6

Jul

SESSION 13

AoPS Math

AoPS Math

Wed 11:00 PM - Thu, 12:30 AM UTCJul 6, 11:00 PM - Jul 7, 12:30 AM UTC

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!!!
SESSION 14

8

Jul

SESSION 14

AoPS Math

AoPS Math

Fri 11:00 PM - Sat, 12:30 AM UTCJul 8, 11:00 PM - Jul 9, 12:30 AM UTC

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!
SESSION 15

9

Jul

SESSION 15

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCJul 9, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns!
SESSION 16

12

Jul

SESSION 16

AoPS Math

AoPS Math

Tue 11:00 PM - Wed, 12:30 AM UTCJul 12, 11:00 PM - Jul 13, 12:30 AM UTC

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!
SESSION 17

13

Jul

SESSION 17

AoPS Math

AoPS Math

Wed 11:00 PM - Thu, 12:30 AM UTCJul 13, 11:00 PM - Jul 14, 12:30 AM UTC

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!
SESSION 18

15

Jul

SESSION 18

AoPS Math

AoPS Math

Fri 11:00 PM - Sat, 12:30 AM UTCJul 15, 11:00 PM - Jul 16, 12:30 AM UTC

We will continue coordinate geometry - now we talk about slopes, perpendicular & parallel lines, and line equations! Practice problems galore!
SESSION 19

16

Jul

SESSION 19

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCJul 16, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns!
SESSION 20

18

Jul

SESSION 20

AoPS Math

AoPS Math

Mon 11:00 PM - Tue, 12:30 AM UTCJul 18, 11:00 PM - Jul 19, 12:30 AM UTC

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.
SESSION 21

20

Jul

SESSION 21

AoPS Math

AoPS Math

Wed 11:00 PM - Thu, 12:30 AM UTCJul 20, 11:00 PM - Jul 21, 12:30 AM UTC

Law of cosines proof! Incredibly important as we delve into quads!
SESSION 22

22

Jul

SESSION 22

AoPS Math

AoPS Math

Fri 11:00 PM - Sat, 12:30 AM UTCJul 22, 11:00 PM - Jul 23, 12:30 AM UTC

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.
SESSION 23

23

Jul

SESSION 23

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCJul 23, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns!
SESSION 24

25

Jul

SESSION 24

Review

Review

Mon 11:00 PM - Tue, 12:30 AM UTCJul 25, 11:00 PM - Jul 26, 12:30 AM UTC

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!
SESSION 25

27

Jul

SESSION 25

AoPS Math

AoPS Math

Wed 11:15 PM - Thu, 12:35 AM UTCJul 27, 11:15 PM - Jul 28, 12:35 AM UTC

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!
SESSION 26

29

Jul

SESSION 26

AoPS Math

AoPS Math

Fri 11:00 PM - Sat, 12:30 AM UTCJul 29, 11:00 PM - Jul 30, 12:30 AM UTC

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!!
SESSION 27

30

Jul

SESSION 27

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCJul 30, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns!
SESSION 28

8

Aug

SESSION 28

AoPS Math

AoPS Math

Mon 11:00 PM - Tue, 12:00 AM UTCAug 8, 11:00 PM - Aug 9, 12:00 AM UTC

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!
SESSION 29

10

Aug

SESSION 29

AoPS Math

AoPS Math

Wed 11:00 PM - Thu, 12:30 AM UTCAug 10, 11:00 PM - Aug 11, 12:30 AM UTC

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!
SESSION 30

12

Aug

SESSION 30

AoPS Math

AoPS Math

Fri 11:00 PM - Sat, 12:30 AM UTCAug 12, 11:00 PM - Aug 13, 12:30 AM UTC

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!
SESSION 31

13

Aug

SESSION 31

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCAug 13, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns!
SESSION 32

14

Aug

SESSION 32

Office Hours

Office Hours

Sun 11:00 PM - 11:40 PM UTCAug 14, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns!
SESSION 33

15

Aug

SESSION 33

AoPS Math

AoPS Math

Mon 11:00 PM - Tue, 12:30 AM UTCAug 15, 11:00 PM - Aug 16, 12:30 AM UTC

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!!
SESSION 34

17

Aug

SESSION 34

Review

Review

Wed 11:00 PM - Thu, 12:30 AM UTCAug 17, 11:00 PM - Aug 18, 12:30 AM UTC

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!
SESSION 35

19

Aug

SESSION 35

Review

Review

Fri 11:00 PM - Sat, 12:30 AM UTCAug 19, 11:00 PM - Aug 20, 12:30 AM UTC

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 :)
SESSION 36

20

Aug

SESSION 36

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCAug 20, 11:00 PM - 11:40 PM UTC

Office hours! Come if you have any questions/concerns!
SESSION 37

26

Aug

SESSION 37

Review

Review

Fri 11:00 PM - Sat, 12:30 AM UTCAug 26, 11:00 PM - Aug 27, 12:30 AM UTC

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 :)
SESSION 38

27

Aug

SESSION 38

Office Hours

Office Hours

Sat 11:00 PM - 11:40 PM UTCAug 27, 11:00 PM - 11:40 PM UTC

Office hours! Ask any questions you need or come to catch up!
SESSION 39

31

Aug

SESSION 39

Review

Review

Wed 11:00 PM - Thu, 12:30 AM UTCAug 31, 11:00 PM - Sep 1, 12:30 AM UTC

More review! After today we'll start AMC questions!
SESSION 40

2

Sep

SESSION 40

Review

Review

Fri 11:00 PM - Sat, 12:30 AM UTCSep 2, 11:00 PM - Sep 3, 12:30 AM UTC

More review! After today we'll start AMC questions!
SESSION 41

3

Sep

SESSION 41

Office Hours

Office Hours

Sat 11:30 PM - Sun, 12:10 AM UTCSep 3, 11:30 PM - Sep 4, 12:10 AM UTC

Office hours! Come if you have any questions or need to catch up!
SESSION 42

7

Sep

SESSION 42

Review

Review

Wed 11:00 PM - Thu, 12:30 AM UTCSep 7, 11:00 PM - Sep 8, 12:30 AM UTC

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!
SESSION 43

11

Sep

SESSION 43

Review

Review

Sun 12:00 AM - 1:00 AM UTCSep 11, 12:00 AM - 1:00 AM UTC

We'll keep doing the AMC 10 from the last session!
SESSION 44

12

Sep

SESSION 44

Review

Review

Mon 12:00 AM - 1:00 AM UTCSep 12, 12:00 AM - 1:00 AM UTC

We'll keep doing the AMC 10 from the last session!
SESSION 45

18

Sep

SESSION 45

AoPS Math

AoPS Math

Sun 12:00 AM - 12:40 AM UTCSep 18, 12:00 AM - 12:40 AM UTC

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
SESSION 46

19

Sep

SESSION 46

AoPS Math

AoPS Math

Mon 12:00 AM - 1:00 AM UTCSep 19, 12:00 AM - 1:00 AM UTC

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!
SESSION 47

26

Sep

SESSION 47

AoPS Math

AoPS Math

Mon 12:00 AM - 1:00 AM UTCSep 26, 12:00 AM - 1:00 AM UTC

Now we will go over Vieta's formulas for polynomials! We'll prove it using factored form, then do some problems!
SESSION 48

27

Sep

SESSION 48

AoPS Math

AoPS Math

Tue 12:00 AM - 1:00 AM UTCSep 27, 12:00 AM - 1:00 AM UTC

Now we will go over Vieta's formulas for polynomials! We'll prove it using factored form, then do some problems!
SESSION 49

28

Sep

SESSION 49

Review

Review

Wed 12:00 AM - 1:00 AM UTCSep 28, 12:00 AM - 1:00 AM UTC

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.
SESSION 50

2

Oct

SESSION 50

AoPS Math

AoPS Math

Sun 12:00 AM - 1:00 AM UTCOct 2, 12:00 AM - 1:00 AM UTC

We are going to talk about transformations today! Today we will devote graphical time to explaining rotations, reflections, and translations.
SESSION 51

3

Oct

SESSION 51

AoPS Math

AoPS Math

Mon 12:00 AM - 1:00 AM UTCOct 3, 12:00 AM - 1:00 AM UTC

Vieta's Alcumus crash course! Today, I'm going to need everyone to be involved :)
SESSION 52

9

Oct

SESSION 52

AoPS Math

AoPS Math

Sun 12:00 AM - 1:00 AM UTCOct 9, 12:00 AM - 1:00 AM UTC

Today we have to start number theory! Topics include: greatest common divisor, least common multiple, modular algebra, and more!
SESSION 53

10

Oct

SESSION 53

AoPS Math

AoPS Math

Mon 10:00 PM - 11:15 PM UTCOct 10, 10:00 PM - 11:15 PM UTC

Continuing number theory: we'll talk about more factoring problems, Diophantine equations, and some important theorems involving modular algebra and combinations!
SESSION 54

17

Oct

SESSION 54

AoPS Math

AoPS Math

Mon 12:00 AM - 1:00 AM UTCOct 17, 12:00 AM - 1:00 AM UTC

We will be starting combinatorics! We'll rush through basic combinatoric arguments, set theory, permutations vs combinations, and basic level problems!
SESSION 55

23

Oct

SESSION 55

AoPS Math

AoPS Math

Sun 12:00 AM - 1:00 AM UTCOct 23, 12:00 AM - 1:00 AM UTC

More review of combinatorics, and we will add in stars and bars and bridge-walking! More Alcumus problems!
SESSION 56

3

Nov

SESSION 56

AoPS Math

AoPS Math

Thu 1:00 AM - 2:30 AM UTCNov 3, 1:00 AM - 2:30 AM UTC

Mock AMC A!
SESSION 57

4

Nov

SESSION 57

AoPS Math

AoPS Math

Fri 1:00 AM - 2:30 AM UTCNov 4, 1:00 AM - 2:30 AM UTC

Mock AMC B!

Public Discussion

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Jun 11 - Nov 4

21 weeks

40 - 90 mins

/ session

SCHEDULE

Saturdays

11:00PM