There are 5 Pillars of Mathematics: Analysis (real & complex), Number Theory, Algebra (Linear & Abstract), Geometry/Topology & Differential Equations; and there are the 4 Food Groups of Physics: Classical Mechanics, Electromagnetism, Quantum Mechanics and Thermodynamics/Statistical Mechanics. These form the Basic Training of those professions; there is no escape! Master the basics, then you will have a solid foundation to build upon. Typically, departments offer "Independent Study" or "Special Project" courses in which you work with a Faculty Member on a topic which isn't covered in the regular curriculum.
Understand the common progression of courses that most universities use for undergraduates. Make sure to take something like intro to proof writing course and get books on that as well as mathematical logic. Make sure to take analysis, abstract algebra, and topology. Make sure to take calc 1-3 and also learn differential forms. You should be able to understand the real fundamental theorem of calculus aka the general stokes theorem. Do NOT sleep on linear algebra. Learn it well and i also suggest multilinear algebra and tensor calculus at least. That's pretty much all the foundation. Make sure you know number theory and category theory and that should be a pretty solid foundation to at least know what you don't know so you can know what to focus on in more detail when you want to get into something more deeply.
Hey, Math Sorcerer, can you make a video about how you take notes during college? Or how do you do them when you are trying to learn math? I believe that it can help many people, including myself. Your wisdom is more than welcome. Thank you!!
Yes. Understanding the basic concepts in a broad area of mathematics should be the prior focus to enhace your knowledges in advanced mathematics. And these can be done through the university courses which can be the most common methods. But to upgrade those skills up, I also recommend discussion with other people. It will enable you to think in a larger scale from different points of views. You can learn from those people and at the same time, can also teach them. So the power of math unites people.
An intro to proofs while might not seem like much help for more advanced math due to its rigid structure would still help you in understanding the language of math at least. One thought has to follow from another when proving things in math. Also a history in math course would help a lot, it will give you perspective and understand where all these seemingly random formulas come from. That's my opinion.
I learned many subjects of math from Wikipedia and from table of contents of math books plus math programming tools. by combining these 3 ingridients it was very beautiful learning journey .and that was before the age of youtube.
My Professors called me a buffoon, as I finished at the bottom of my class. My greatest fear was that they were right. It's what motivates me to keep trying to know what they know.
@@martinhawrylkiewicz2025 yeah. True. It's a huge book but has a very conversational tone. Btw, his wife read the manuscript and edited it except for the math parts. lol.
@@StaticBlaster I'm sticking with How to Prove it. I love it how Velleman explains things and gives you the motivation or his thought process behind every proof.
@@martinhawrylkiewicz2025 I actually have that book too. I've had the second edition since 2011 when I dropped out of college. I should go through it so that I have the foundational logic I need to learn python and other programming languages.
cooper,you asked my question bro i am first a year student at saint petersburg state uni and i am studying maths and cs. The maths is a lot because i have real analysis,abstract algebra,geometry and topology,maths reasonsing and proofs,number theory and discrete analysis. and Russians approach maths differently they have their own unique ways of solving maths being an international student here i have to master the maths plus their techniques some topics they are not even on the internet its only a russian who knows how to do it and i am studying in russian so its diffucult and depressing and time consuming.
Improve the basics of mathematics and when you confront advanced mathematical questions. teach yourself how to solve the questions if you have no access to an expert..
Yes mathematics is the language of univers so you must invest in its the god verses in the univers yes language mathematics and writing are the fundamental variabels in the existence of the human being ...ZARFA THE SON OF KAIDAR THE ALGERIAN ..
that's probably stuff from higher grade or competition maths.... not advanced in the sense of pure mathematics.... I'm curious what areas the syllabus contains?
There are 5 Pillars of Mathematics: Analysis (real & complex), Number Theory, Algebra (Linear & Abstract), Geometry/Topology & Differential Equations; and there are the 4 Food Groups of Physics: Classical Mechanics, Electromagnetism, Quantum Mechanics and Thermodynamics/Statistical Mechanics. These form the Basic Training of those professions; there is no escape! Master the basics, then you will have a solid foundation to build upon.
Typically, departments offer "Independent Study" or "Special Project" courses in which you work with a Faculty Member on a topic which isn't covered in the regular curriculum.
I've never heard anyone say 'food groups of physics,' but it sounds good-very creative.
@@Neo-Reloaded It's a heck of a diet!
Having a foundation in mathematics before high-level math is super important.
Understand the common progression of courses that most universities use for undergraduates.
Make sure to take something like intro to proof writing course and get books on that as well as mathematical logic.
Make sure to take analysis, abstract algebra, and topology.
Make sure to take calc 1-3 and also learn differential forms. You should be able to understand the real fundamental theorem of calculus aka the general stokes theorem.
Do NOT sleep on linear algebra. Learn it well and i also suggest multilinear algebra and tensor calculus at least.
That's pretty much all the foundation. Make sure you know number theory and category theory and that should be a pretty solid foundation to at least know what you don't know so you can know what to focus on in more detail when you want to get into something more deeply.
Hey, Math Sorcerer, can you make a video about how you take notes during college? Or how do you do them when you are trying to learn math? I believe that it can help many people, including myself. Your wisdom is more than welcome. Thank you!!
Persistence and perseverance is the key
Yes. Understanding the basic concepts in a broad area of mathematics should be the prior focus to enhace your knowledges in advanced mathematics. And these can be done through the university courses which can be the most common methods. But to upgrade those skills up, I also recommend discussion with other people. It will enable you to think in a larger scale from different points of views. You can learn from those people and at the same time, can also teach them. So the power of math unites people.
An intro to proofs while might not seem like much help for more advanced math due to its rigid structure would still help you in understanding the language of math at least. One thought has to follow from another when proving things in math. Also a history in math course would help a lot, it will give you perspective and understand where all these seemingly random formulas come from. That's my opinion.
I learned many subjects of math from Wikipedia and from table of contents of math books plus math programming tools. by combining these 3 ingridients it was very beautiful learning journey .and that was before the age of youtube.
the never stop train.
Well poor conductor, hope his payed by the hour.
For real
How to learn advanced engineering math?
I will make a video on this!
My Professors called me a buffoon, as I finished at the bottom of my class. My greatest fear was that they were right. It's what motivates me to keep trying to know what they know.
Book of Proof by Hammack (studied last year) and How to Prove it by Velleman (current study). Enough said.
what about the book by Jay Cummings??
@StaticBlaster it's ok too but I found it too big size wise to carry around, and a bit too "chatty"
@@martinhawrylkiewicz2025 yeah. True. It's a huge book but has a very conversational tone. Btw, his wife read the manuscript and edited it except for the math parts. lol.
@@StaticBlaster I'm sticking with How to Prove it. I love it how Velleman explains things and gives you the motivation or his thought process behind every proof.
@@martinhawrylkiewicz2025 I actually have that book too. I've had the second edition since 2011 when I dropped out of college. I should go through it so that I have the foundational logic I need to learn python and other programming languages.
cooper,you asked my question bro
i am first a year student at saint petersburg state uni and i am studying maths and cs. The maths is a lot because i have real analysis,abstract algebra,geometry and topology,maths reasonsing and proofs,number theory and discrete analysis.
and Russians approach maths differently they have their own unique ways of solving maths being an international student here i have to master the maths plus their techniques some topics they are not even on the internet its only a russian who knows how to do it and i am studying in russian so its diffucult and depressing and time consuming.
Which book is good to initiate the journey of topology
Recently discovered Evan Chen's OTIS book on the web, learning lots from it
Improve the basics of mathematics and when you confront advanced mathematical questions. teach yourself how to solve the questions if you have no access to an expert..
I love your hair
Yes mathematics is the language of univers so you must invest in its the god verses in the univers yes language mathematics and writing are the fundamental variabels in the existence of the human being ...ZARFA THE SON OF KAIDAR THE ALGERIAN ..
Hey math guy, face reveal when?
You look like jeff bezos
He kinda does lol but Jeff bezos w hair
first!
I'm from India state Assam .And I have taken advance mathematics in 9th and 10th grade in optional
that's probably stuff from higher grade or competition maths.... not advanced in the sense of pure mathematics.... I'm curious what areas the syllabus contains?
@doofus8 yeah it's amazing but also a little bit harder .