Can we become mathematicians by way of self-study? (Part 3)

In response to the question "should I become a mathematician" , the problem is whether you love math with a passionate love, have admiration and patience for math or not. If you love math, love it. If you like the idea of becoming a mathematician, you should set a vision to turn math into your hobby. When you have a vision, what knowledge do you need to pursue to pursue a career in math?

Please read to part 3, which is also the end: the path to becoming a self-taught mathematician. The series summarizes the opinions of readers Quora.com, one of the leading question and answer websites in the world.

Matthew Graham , a bachelor of math and statistics and a career in research, offers some very practical advice to math lovers like him.

Matthew graduated from the University of Saint Louis (Missouri), ranking 140th in the United States and top 500 in the university rankings of Academic Rankings of World Universities 2018.

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Readers Matthew Graham, a bachelor of mathematics and statistics at the University of Saint Louis, Missouri, USA

According to Matthew, to become a self-taught mathematician, you need to have the following conditions: budget to buy books, time (a lot of time), absolute determination and patience, which is essential Core is work ethic. And you have to be willing to spend a lot of years in your life learning math, because that's what you need to reach the level of modern mathematician.

Matthew suggested a number of subjects as follows: starting with basic subjects such as elementary algebra, geometry, trigonometry, then learning how to write proof. After these basic subjects are calculus, abstract algebra, complex variables.

Once there is a foundation, there are many ways for you to pursue such as differential equations, probability / statistics, combinatorics / graph theory, learning topology, etc.

Proving to be an extremely basic skill in mathematics, you cannot call yourself a mathematician but never have a proof. You need a solid foundation for this proof of skill, a skill that is difficult to fully describe its importance. Without basic trigonometry / algebra and proofing skills, you will not be able to become a mathematician in the future. Read some good books on this topic.

For advanced mathematics, Matthew suggests a number of books and authors such as Michael Spivak's book of integrals, abstract algebra by John B Fraleigh, David S. Dummit and Richard M. Foote, a book. About complex variables is Visual Complex Analysis.

Integrating is an easy challenge, so you need to learn slowly and firmly. Good books will help you learn a lot and go at the right speed. This is not a race, all of these documents are very difficult, go slow and firm to ensure mastery of the basic concepts. You do not need to rush.

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In Matthew's practical thinking, today, becoming a self-taught mathematician is not feasible.(Artwork: Fiverr)

The best option is to join classes at a local community college if you can. Online classes can also be effective, but it will still "kick" the ball back to math completely.

If you really pursue the suggestions on books and research areas above, expect one year for each. You have to go slowly and make sure you really understand everything in the book. Only learn a part in every two to three days and solve at least 20 problems for each section to reinforce and develop knowledge. Math Stackexchange, reddit and quora will be your companion in this.

In Matthew's practical thinking, today, becoming a self-taught mathematician is not feasible. If you want to publish a study without a PhD in math, forget it. Maths are too deep roads for you to simply select them after just reading through some research. First, you have to take the basic part in each subject!

And then, it's about time that you can't simply choose a textbook anymore. Matthew had just graduated from college and was preparing to study mathematics so he could not recommend a master's book better than the typical books of Rudin, Munkres, Dummit, Foote.

In general, to become a mathematician, you need to learn the appropriate graduate research opportunities and interact with the areas of active research . You simply can't go there yourself in today's world. You need instructions from an expert.

The Academic Rankings of World Universities ranking (ARWU ) we refer to in this series is one of the three most influential and well-known university rankings in the world today, along with two tables of QS World Universities Rankings and Times Higher Education World Universities Rankings-THE. When it was born in 2003, ARWU was compiled by Shanghai University of Transport (China). Since 2009 ARWU has been implemented and managed by Shanghai Ranking Consultancy (Shanghai Ranking Consultant), an independent organization of higher education. ARWU focuses on academic excellence and academic achievements - the highest level of research activity at universities such as: the number of Nobel Prize winners and Fields medals , an index of social science and extension, the number of articles published in Nature and Science .