He's in 10th Grade and Wants to Learn Math BEYOND High School

In this video I answer an email I received from a viewer. He is in 10th grade and wants to learn math beyond what is learned in school. I recommend two books, The Book of Proof by Hammack and How to Prove It by Velleman. Do you have any advice? If so, please leave a comment below.

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[benjamincabrera]

My son had a similar situation some years ago. He felt the pacing and depth of high school math frustrating. I found a local program that allowed concurrent enrollment at the local state university. An SAT math minimum had to be reached but it was not too steep...maybe a 600 math or so. I continued purchasing math books of all types and he particularly liked "How to Solve It" by Polya and so the pursuit of his math interest became our mutual endeavour. He took numerous math courses that placed him well ahead of his peers in High School. By the time he approached the beginning of 12th grade the local state univeristy offered him a full scholarship but he opted to attend MIT instead. He credits his math ability to a lot of hard work but also great source materials. In the end I may have spent up to $5000 in books but it saved me tons on college expenses. He recently graduated with a PhD in Mechanical Engineering, travels the world solving interesting problems, and completed his entire education not one cent in debt. The power of math education.

[brandonfiennies]

Another reminder. Do math Olympiad problems especially word problems. They help you develop better problem solving skills. Don't give up though even if it's difficult.

[yuto]

Currently also in 10th Grade, though I don't show interest in (Pure) Math, it still is my best performing subject. I'm also planning to take Physics and Engineering in college by the time I graduate in the next two years. My only tip for anyone, young and old alike, don't let age, money, or time ruin your passion, and as the Nike slogan says: Just do it.

[lukeatlas]

I recommend Advanced Precalculus by Daniel Kim, it’s a great preparation for undergrad since it contains many of the topics on those books including Advanced Trigonometry, Linear Algebra, And some Calculus!

[gvi]

Take dual credit courses or community college on the weekends? Community college doesn't have high school requirements just immunization

[optimalcodex]

Hey I think that's great idea to start doing math as a hobby outside of school! Firstly, probably start looking into competition math problems, theyre difficult, but they are fun! Also, starting with topics like Set Theory or Graph Theory is also fun, I would recommend art of problem solving or dover books.

[jacobharris]

I was deeply interested in math and science in high school but never made much of an effort to go above and beyond the minimum curriculum until my senior year when I took brief calculus. I wish I was more like this kid early on. If I really pushed myself I could have probably done calc 1-3, linear algebra and differential equations before college.

[noam]

Kahn, the answer given to your question, how do I improve myself, seems actually broader than being restricted to maths alone. Though I think the answer expressed in this video is a good start. I will address myself to the larger question.

I had a similar drive and goal, as you stated for yourself. When I was your age, there were no personal computers or smart phones, and no internet.

What I did have was time on the weekends, holidays, and summers. I had a part time job.

I used to spend a lot of time in libraries and book stores. I spent time learning what my interests were, and engaged myself in reading on topics that interested me, and there were many. I thumbed through many books on those places, and learned a lot. Other books required a more thorough reading. Those I would bring home and read. I also took chances and read books in other areas I wasn't familiar with.

Psychology, space science, philosophy, religion as philosophy, all the major ones. It helps to learn world views of many peoples of the world. I read also on the edge of acceptable knowledge, proof of afterlife, souls, etc. I read also about maths, history, arts, and many other topics.

The point is gather knowledge and wisdom, mostly through books. Publishers are careful about the quality of the works they produce, and provide editors for authors, so the expression is smooth and concise, at least more than without such editing. This method will train you to recognize high quality information.

Next strategy, when opportunities come up to speak with adults with interesting jobs, ask if they wild speak with you about it. Most will engage with you over such a request. Try to ask intelligent questions, and always be respectful of them and their time, and thank them for their efforts.

Lastly, look to develop new skills by finding after school hobbies, maybe photography, woodworking, cooking, etc. It's always gif to learn new skills. There are free or low cost courses to be found both in person, and online.

Book wise, I have a few introductory suggestions.

HOW TO MAKE FRIENDS AND INFLUENCE PEOPLE - DALE CARNAGIE

THE POWER OF POSITIVE THINKING - NORMAN VINCENT PEALE

CREATIVE VISUALIZATION- SHAKTI GAWAIN

HOW TO STUDY -RON FRY

Add the above to your list. These books have stood the test of time.

Here are the names of some free book websites. They are older, in the public domain, but many are still worth the time and effort.

Project Gutenberg
The Internet Sacred Text Archives
Great Books Of The Western World
Good Reads - for more current suggestions

I hope this helps.

[maxmontauk]

My simple advice is Don't Ever Give Up! - There are so many ways to learn available - if one particular avenue isn't working out, set it aside (maybe come back to it another time) and try a different approach - this works for me.

[abolfazlmohseni]

In my opinion the books that sort of proof is soon for the student who in 10th grade and its better to study discrete mathematics because it is so useful and the proof books actually have problems that you must know algebra, pre-calculus, discrete mathematics and also some geometry. the discrete mathematics its start with logic can change his perspective to lesson has in Hight school then study the counting lessons can help him in the possibility problems and study the problems that improve his intelligence. 😊

[mvdrider]

Thanks! Great content as always and excellent question from the viewer 🙌🏻💯

[Sorobai]

Another great vid with good advice. Thank you

[prof.sonandrwer]

Wow... This video really helped me a lot....

[katto]

I really like the proofs idea - you don't learn that type of thing in high school. My son didn't get to do any proofs until post graduate study. I think that doing things outside the school curriculum is a good idea - otherwise senior high school work will become boring. It's also a great time to develop skills that employers desire.

I would suggest that getting yourself ready for college/university study so that you have the necessary skills to avoid a steep learning curve.

Anything in the pure mathematics realm is going to be good (most high school work is applied unfortunately). To that end maybe do some number theory which is a great foundational subject. You could also have a look at basic level abstract algebra and topology. Also linear algebra (as long as you have the prerequisite knowledge such as cartesian plane and know a bit about vectors etc). Also maybe delve into statistics (which isn't covered in any depth during high school).

Another idea is learn about further mathematics in science subjects covered at school (and maybe delve into the proofs of the equations that are just given to you). It gives you a greater understanding of the topic - science, physics and chemistry in particular.

Another idea is to learn or improve (depending on where you are at) your coding and programming skills. Also learning how to type mathematical symbols ie LaTeX is also a great idea. You could also learn how to use mathematical software such as maplesoft, R (stats) and python or C programming etc.

You could also join a local club such as astronomy, robotics, computing etc. There are also some summer and winter schools at various universities. They are often targeted at gifted high school students. Maybe your local college/university has some public lectures that you could attend. There are a heap of such things on youtube - it would be more about exposure to new ideas rather than needing to understand everything. There are also maths competitions available for your age group - google should be able to help with that.

[brandonfiennies]

This is the video I wish I had seen last year😭

[willlancer]

Hello to the questioner,
I am currently in high school as well, self-studying multiple math and physics courses. AoPS (a website that also sells books and courses) is going to be key if you want high-level fundamentals. Outside of that, you can either progress faster through the traditional curriculum (calc 1, 2, 3, linear algebra, diffeqs, partial diffeqs), or you could step into discrete. The math sorcerer’s vid on “how to learn math from start to finish” is great for discrete recs. You could also take courses at uni so it looks good on your transcript or if you prefer in-person learning. Good hunting.

[bruh____]

Damn, im in the exact same position as him, I'm done with 10th grade final exams tho and i will definitely try to check these books out; thank you!!

[budgarner]

Take the Math Sorcerer's advice on a proof and logic study. Geometry as a course of study was originally designed to teach the proof and logic behind the measurement of the earth and its contents. Work to be the best visual learner you can; pattern recognition is a critical skill to strengthen. Work with and create your own tables of information. Look for trends; defend your interpretation. Be broad in your approach to realize possible outside influences that are not given in the data. It's a shame that there's not an AP study for proof and logic for you. In the US because it's "too hard" proofs have gone from half of 10th grade geometry in the 60s/mid 70s to 3 weeks by the late 80s. I had lots of problems with the flow and structure of proofs at the start. I just didn't get the connections. Near the end of the section, I finally got the hang of it and paid off in college, programming and workplace analytics. Current curriculum gatekeepers do not know their math history/curriculum. Don't let their lack of knowledge or interest keep you from investigating on your own.

[erthx]

10th grade was 1984 for me, Back then fascinated with why 0! = 1. My algebra 2 teacher Rufus Dickinson (BTW, my favorite teacher of all time) told me he'd seen this 40+ years ago in college, but couldn't remember it.
Years went by, I contacted him in 2008. I told him I was sort of delivering as long overdue homework assignment. I brought up the Euler-Gamma function and its role with the factorials, made for an awesome reunion.

My advice to Kahn is to always keep his passion alive for mathematics. Life definitely will get in the way, work, money, relationships, & social drama. The late Dr. Dominic J. Monetta stated that we believe we are engulfed in a time management crisis, but this is certainly a priority management issue. On Dom's behalf, this may seem like a "no duh statement, " My question becomes, "Why don't most people exercise this principle?"

On a final note, If we appeal to Maslow's hierarchy, the Math Wizard seems to be reaching for self-actualization mathematically, which would be a good fit for Khan.

[pythonstudios]

“Only a great fool would reach for what he was given.”
Take what they give you in school, but reach beyond that. Find topics that are engaging and ones you may not be able to easily find a class on. That helped me through a very tedious master’s program and allowed me to apply what I was learning in class in original ways that my classmates were unable to do.