Learning Math Proofs, Real Analysis, and Abstract Algebra

In this episode of my podcast I answer a question I received from a medical student. He wants to learn advanced mathematics and is looking for advice. I give tips for learning mathematical proofs, advanced calculus, and abstract algebra.

(these are my affiliate links)

(these are my affiliate links)

***********Math, Physics, and Computer Science Books***********
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.

If you enjoyed this video please consider liking, sharing, and subscribing.

There are several ways that you can help support my channel:)

************Udemy Courses(Please Use These Links If You Sign Up!)*************
Abstract Algebra Course

Advanced Calculus Course

Calculus 1 Course

Calculus 2 Course

Calculus 3 Course

Calculus 1 Lectures with Assignments and a Final Exam

Calculus Integration Insanity

Differential Equations Course

Differential Equations Lectures Course (Includes Assignments + Final Exam)

College Algebra Course

How to Write Proofs with Sets Course

How to Write Proofs with Functions Course

Trigonometry 1 Course

Trigonometry 2 Course

Statistics with StatCrunch Course

Thank you:)

[Cmon_amaan]

Just got an A in proofs. Headed to real analysis. Been watching you for years, on my journey to become a math teacher, thanks Math Sorcerer.

[thesunnydk]

I am a medical doctor in the UK recently graduated from medical school and I am studying mathematics part time at a local uni while working full time as a clinician. I really encourage any other clinicians out there who are thinking of pursuing mathematics to go ahead. It will be challenging but it is worth it. It is a completely different thinking skill compared to medicine and I am sure it will be beneficial especially if you are interested in academic medicine. I think it is a shame that medicine, being a STEM subject, has almost no maths training.

[Greekr]

I am a medical doctor who used to be an engineer. I'm trying to relearn math and i really enjoy the abstract algebra book by Saracino and your Udemy course. You make it look like learning is a game.
You're inspiring, keep up the good work. All the best from Canada!

[dhickey]

Thank you, Math Sorcerer. Math proofs are as important to critical thinking as the alphabet is to learning to read. It should be essential knowledge in a modern world.

[douglasstrother]

I recommend going "Old School". Dive into good ol' Geometry: pencil, compass, straightedge; spirals & conic sections.
Go full-throttle "Vitruvian Man"!

[martinhawrylkiewicz]

Great vid as always. I have been studying How To prove It by Bellman (3rd Edition) based on your suggestions for months and now I started chapter 5 on functions. I try my best to do it sequentially, from the beginning, without skipping any sections and doing all the exercises. really love this book and Velleman's approach to proofs. He explains things so well, breaks everything down and does commentary after the proof about the motivation behind it, the thought process etc.

[ussdfiant]

I am a physician with med school well behind me. Currently self studying my way through Algebra for the college student by Blitzer and Hammack’s Book of Proof.

[angrycat]

I stopped my math journey for a while. I'm retaking it with book of proof, Im just a bit over half of chapter 1 doing almost all exercises, I'm enjoying it so far. Also, I'm feeling rusty on derivatives and integrals so I'm reading that book your recommended on differential equations (nagle, saff, snider). Thank you.

[JoeyV]

I'm doing what I think I can do prepare for real analysis ontop of doing research this summer. It is overwhelming, and I'm worried sick over the fact I will completely flunk this class. The jump in logic from an intro to proofs class to real analysis seems to be quite the jump. Wish my luck haha, thanks again Morcerer for another great video!

[Taylor-rxyb]

Great video! My first advanced calc course didn't have a book, but I used Understanding Analysis by Abbott. It was a great help and I would really recommend it. Now the second semester of advanced calc did follow Fitzpatrick for the multidimensional stuff. I have not looked at that for a while now, but I recall it being nice (despite having a relatively poor professor). I made the poor decision of taking the grad level algebra course before the undergrad one (which has been ok in the long run but was hard then) so I don't have undergrad books for that. However, it is a good lesson to learn to not bite off more than you can chew. It can make you stronger sometimes but it requires pain.

[TinyMaths]

Thanks for the book recommendation; I'm glad it's a PDF. Been working through a few calc problems daily so it's time to add 'one' daily proof problem in the mix.

[julianwilson]

Great video and advice! If the email writer or anyone else is interested in learning mathematics on top of their medical studies, another option (one of many) would be to study applied math. All kinds of topics from differential equations for mathematical biology/physiology to Fourier analysis (say for signal and image processing) could be of interest. Good luck!

[walterloehrmann]

Thanks. Got the book of proof pdf for free. Very nice project.

[jbbentley]

Wizard, just a few days away from the start of another semester. I’m taking the max class load and trying to petition to get more. If I’m not taking maths I get bored and feel no sense of enjoyment asides my garden.

[shiminglu]

Also you can find the requirements for a math degree from a top university, they will have open source outlines. Try to dive into it, there may contain some recommended textbooks to read. It may be beneficial to you : )

[hemberry_]

huge thanks, i choose maths as my second degree alongside medicine (you get into medicine only by choosing two degrees in france, a bit tough to be honest) I'm just horrible at writing proofs and I have an exam on that, this book is really useful

[FriazKhalil]

Hello, can you help me? I learn mathematics from a phone as well as from the book Algebra 1. I mean, I learn this rule from YouTube, then I solve that rule on the book Algebra 1. Is this a correct way? Nor should I rely on a book

[amorfati]

Are there subjects that have a slightly lower barrier to entry than abstract algebra, or is this path you've laid out the best way to go about seriously studying math? I ask because I am currently learning proof writing, and some more discrete math, and I see things like graph theory, which seem relatively new, and I think it would be really cool to be able to look at a math journal on something like graph theory or combinatorics and understand the current state of what the thinkers in these topics are currently working on.

[nigerianking]

How can learn how to do mathematics for the first because I not good at it I failed my college class three i reall feel bad I pass at all please 🙏 help me why I’m trying to earn my degree in medical lab technician 🧑🏽‍🔬

[davidhamelehh]

if you pass real analysis and abstract algebra you can pass everything. hardcore classes (and, if you have an hardcore teacher... thats gg's)