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Introduction We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order. So in order to answer those questions, I have decided to make a list of topics a mathematician should ideally know and what prerequisites the topics have. Basic stuff Of…
This is a sequel to my posts on self-studying mathematics. I have already given a very detailed road map on how to study high school mathematics and calculus. In this post and the next ones, I will try to give a very detailed road map on how to self-study analysis to reach a high level….
We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order. So in order to answer those questions, I have decided to make a list of topics a mathematician should ideally know and what prerequisites the topics have. Calculus After high school…
How to self-study mathematics? People self-study mathematics for a lot of reasons. Either out of pure interest, because they want to get ahead, or simply because they don’t want to take formal education. In this guide, I will try to provide help for those people who chose to self-study mathematics. Is it even possible…
Introduction I am convinced students learn Calculus far too late. In my view, there has never been a good reason for this. In the US, they go through this sequence of Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus, Calculus 1, and Calculus 2. But is this required? Recently I came across two books that turned…
Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say 1/trillion to the power of a trillion) can be thrown away because they are negligible. That way, when defining the derivative, for example, you do not run into 0/0, but when…
I often read questions about our classification scheme that we use on physicsforums.com to sort posts by science fields and subjects, what has to be studied first in order to learn something else, what is a good way through physics or mathematics in self-study or simply about the desire to understand, e.g. general relativity…
What is the ambiguous case? In high school geometry, the idea of proofs is often first introduced to American students. A common task is to use a basic set of rules to prove two triangles are congruent, which is a fancy way of saying they have the same side lengths and the same angles. Phrases…
We asked our PF Advisors to tell us their most memorable or influential textbook and why. Here are their responses… Thanks to all the PF Advisors that shared their favorite textbook. We have more questions for them in the near future. Stay tuned for another “Ask the Advisors”!
Give us an early bio on yourself Well, I was born and raised near Dallas, Texas as the only boy of 4 children. I grew up with 3 sisters, though I had another sister, 3 stepsisters, and a stepbrother that I did not live with. I’m only 10 minutes younger than my twin sister…
There are three big parts of mathematics: geometry, analysis, and algebra. In this insight, I will try to give a roadmap towards learning basic abstract algebra for self-study. This includes the study of groups, rings and fields, and many other structures. Prerequisites The requirements for self-studying abstract algebra are surprisingly low. Basically, you should be…
For several years already I have been trying to help students who have been self-studying math. I did this completely free with no compensation for me. I saw this as a very enriching experience. Most of the people I helped came from physics forums. I usually contacted them and told them I might be able…
If you wish to follow this guide, then you should know how to do analysis on ##\mathbb{R}## and ##\mathbb{R}^n##. See my previous insight if you wish to know what kind of topics you need to know and for suggestions of books: https://www.physicsforums.com/insights/self-study-analysis-part-intro-analysis/ Also in many parts, you should be comfortable with linear algebra, see my…
This insight is written for high school students who don’t feel very challenged by their high school courses. Or maybe those high school students who want to have a taste of what university math is like. The good news is that you don’t have to wait until university to see exciting mathematics, you can learn…
Geometry is one of the oldest parts of mathematics. It has been studied and advanced by the greatest minds humankind has to offer. It has been described as a subject of great beauty. How do we approach such an amazing work of art as a student? In this section, I will attempt to give you…
Part III: Mathematical Preparations In most universities in the US, a student must have a declared major by the end of his or her second year. So this is an important transition – making the commitment in a particular area of study. By now, if you have followed the first two chapters of this…
Introduction For the past few days, during my summer break, I have been intensively self-studying mathematics (namely number theory) for several hours each day without having prior experience in theoretical math. The struggle of learning is not unique to mathematics; during my first year of computer engineering (which I had just completed at the time…
Meet a Mentor is a fun series to help you get to know your wonderful Mentors better. Constructive questions and comments are welcome! Today we meet: DaleSpam Give us a brief history of DaleSpam I have moved around a decent amount during my life: Arizona, Indiana, Colorado, Texas, Michigan, Utah, Ohio, and North Carolina. With all…