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Questions tagged [advice]

Questions asking for advice on various mathematical matters. Be careful that your question is answerable, and also that it is not a polling question (e.g. "What is the best / your favorite way to...").

105 questions with no upvoted or accepted answers
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171 views

Bertsimas & Tsitsiklis's Linear Optimization book

I just want to ask a question about the "level" of this book. In the book's preface it is written that the only prerequisite is knowledge of Linear Algebra. Is this book good for undergraduate ...
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1answer
131 views

To prove: a product of profinite groups is again profinite.

I got stuck on this syllabus about abstract algebra: Let $J$ be a set and $\{ \pi_J \ : \ j \in J\}$ be a collection of profinite groups. Show that $\prod_{j \in J} \pi_j$ is again profinite. ...
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937 views

Solutions for “What is Mathematics?” by Richard Courant

I am currently reading through Courant's "What is Mathematics?" Most of the time I am not taking the exercises too seriously, given that I am reading this for pleasure, and that often my solutions are ...
2
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0answers
188 views

Matrix Calculus

My school offers Matrix Calculus class next semester. I have never heard about this subject before and got intrigued. After a short chat with professor I found myself unable to get rid of suspicion ...
2
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0answers
229 views

Is there a companion to the book 'A Synopsis of Elementary Results in Pure and Applied Mathematics' by George S. Carr?

A Synopsis of Elementary Results in Pure and Applied Mathematics by George S. Carr is as most of you probably know a book that was famously used by the great mathematician Ramanujan. It is said he ...
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0answers
78 views

What topics should I study to understand this document?

Background I'm trying to understand a document I found online. The reason I'm reading it is because I need to translate the Nedelec element into code for my research. Problem My background is in Food ...
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0answers
44 views

How to relate two integration contour?

How one can relate two integration contour? For example if I have an integration contour like $\int_{-a}^{a}f(x)dx$ here let say a=infinity. How I can say that the integral $\int_{2}^{3}f(x)dx$ is a ...
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0answers
165 views

self-study hints

A question to those who took rigirous courses like math 25 (Harvard), MATH 295-396 Michigan and etc Being not able to collectively discuss problem sets from the course, as those who involved in ...
2
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0answers
102 views

My attempt to gather mathematical spaces in a drawing

There are many spaces (Sobolev, inner product spaces, etc.) that I am not using on a daily basis, but have to recall their definition from time to time. So I decided to draw a synthetic scheme of the ...
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36 views

Finished Real Analysis (baby Rudin syllabus), what to read next?

My question is more of a strategic type. I have recently finished learning about most of the topics in baby Rudin (PMA), but from a different textbook, at my school. As you can imagine, I haven't ...
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0answers
43 views

Math Lesson Name

I live in a developing country and the education systems in my country is not very good. I'm studying in second year of high school and I always wanted to improve my math and others skills so I learn ...
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0answers
49 views

Prerequisites for the complex analysis part of Rudin RCA

What are the prerequisites for the complex analysis part of Rudin Real and Complex analysis book? Is it possible to start studying the complex analysis part with the knowledge acquired from the first ...
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0answers
58 views

Are there huge differences between textbooks?

I am about to start my first year in college. I am not a class type student. I like going deep while studying myself and understanding the reasons, beauty behind these ideas. I have been looking for ...
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0answers
64 views

(soft question) Summer Math Project for Undergrad

I’m an undergraduate math major and am currently a rising sophomore. In my first year, I had a fair bit of experience with real analysis and linear algebra (but nothing fancy). I have some free time ...
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0answers
34 views

Poincare's Inequality

Assume $\Omega \subset L_d$, for some $d > 0$. Then, for all $u \in W^{1,q}_0(\Omega)$ $1 \leq q \leq \infty$ , $\left \|u \right \|_p \leq (d/2)\left \| \nabla u \right \|_p$. Prove that the ...
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0answers
121 views

Any good alternatives to Inverse Symbolic Calculator?

Inverse Symbolic Calculator (ISC for short) is down https://isc.carma.newcastle.edu.au/ :-( What would you use instead of this resource now? Wolfram alpha can give answers in simple cases, but from ...
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1answer
25 views

How do I determine the interval over which my error calculation should be conducted?

I've been instructed to find the values of x for which the function $f(x) = e^{-2x}$ may be approximated by the Maclaurin series $1-2x+2x^2-\frac{4}{3}x^3$ with an error of less than 0.001, but no ...
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3answers
83 views

Best resources for learning/practicing beginning topology?

I'm an undergrad with minimal experience in proof-based classes, and I'm in a pickle with a current course. Normally, I have trouble understanding and/or retaining information during lectures, so I ...
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0answers
148 views

What subjects to study to improve “mathematical maturity/fluency” to learn more efficiently?

tl;dr: What advanced math subjects should I study to be able to learn new material more efficiently? I recently finished undergrad as a computer science major, but in my current work there's a ton of ...
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0answers
30 views

Computing with large vectors and matrices

I'm working on a project that requires the use of large data sets; vectors and matrices with millions of entries. Normally I've done my projects (small scale stuff) with Matlab and never had an issue. ...
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0answers
67 views

Confusion about number theory topics

So, my background in Number Theory is - Elementary Number Theory(that I did mainly from David Burton's text) and Serre's A course in Arithmetic(first half on algebraic methods that included p-adic ...
1
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1answer
512 views

Spivak's Calculus for a soon to be physics undergraduate.

I'll soon start my undergrad. studies in physics and because of that I picked up Spivak's Calculus a while ago to get a solid foundation in single-variable calculus before I start my studies. However, ...
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0answers
207 views

Good books on Algorithms for a math major without any programming experience?

I couldn't find this question anywhere else so it may not be apt. I am an undergraduate mathematics major and during my discrete math class I really enjoyed the study of algorithms and recursive ...
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2answers
104 views

Dealing with computations that are tedious and time consuming

In attempting mathematics homework question one of the greatest redundancies I generally face is having to deal with long winded and tedious computations. For instance, in the field of Quantum ...
1
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0answers
220 views

Number of Magic squares and their applications

A magic square is a square array of numbers consisting of the distinct positive integers $1, 2, ..., n^2$ arranged such that the sum of the $n$ numbers in any horizontal, vertical, or main diagonal ...
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0answers
73 views

Partial Differential Equations Methodology

I am currently studying PDE's i got an almost standard methodology for the First order PDe's mostly using the characteristic's Method.Now Im on the Second order Pde's .So i wanted to get some things ...
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0answers
1k views

Partial Differential Equations Course And Differential Geometry Prerequisites

Is the ordinary differential equations course a prerequisite for the partial differential equations course for a person who has passed the integral calculus course? Is it really required to have ...
1
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1answer
252 views

prove normality of famlity of analytic functions

I already proved normality for meromorphic functions that omit 3 values. I'm trying now to prove normality of family of analytic functions that omit two values. Is there any way to deduce any one of ...
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31 views

¿Has the proof of Theorem 1.21 of Principles of Mathematical Analysis by Walter Rudin a meaning?

I did the proof of this theorem a slightly different some time ago, but, I really forgot almost everything and the problem is that, I understand the body of the proof, but, I don't understand why he ...
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26 views

Having hard time solving inequality problems, what should I do?

I can't see the operations and symmetries required to solve a lot of those problems, which is extremely frustrating for me. I am trying to learn from "Inequalities- a math olympiad aproach" , and ...
0
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1answer
36 views

Hall & Knight's “Elementary Trigonometry”: When to add it (or similar) to my self-study to prepare for Calculus?

Sorry if this has been posted before. If so, please direct me to the previous version so I can delete it. I saw this PDF of Hall & Knight's 1906 "Elementary Trigonometry" (archive.org link). I ...
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16 views

(Soft Question) Coming up with elaborate arguments

I struggle with solving problems that require elaborate arguments, basically anything more than a few lines. It's not that I struggle to understand long/hard arguments: I'm able to understand hard ...
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0answers
67 views

What is it like to be a pure mathematician?

I'm an engineering student, currently in 3rd year. I have developed a fair bit of interest towards pure mathematics. 1. My question is when should one think about having a career in pure mathematics? (...
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31 views

How to develop abstract thinking and problem solving skills?

I am currently doing post graduation in Industrial Mathematics. During my graduation years, I did not have much trouble in understanding the theorems or I should rather say, the arguments in the ...
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0answers
20 views

Advice on mathematical and physical sources & dictionaries with the indexes (filters)

Could you recommend some resources or dictionaries on mathematics and physics with terms filtered by thematic indexes, such as the Compendium of Chemistry Terminology (a.k.a. the IUPAC Gold Book) or ...
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65 views

Suggestion for course taking

(Summary) There will be a reading course using Differential Geometry: Bundles, Connections, Metrics and Curvature by C.Taubes. What is the prerequisite for this book? Is its contents something that ...
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0answers
24 views

Learning modular form for Riemann surfaces

I am currently learning Riemann surfaces and am wondering if learning modular forms would be helpful (like improving my understand, introducing more useful tools in Riemann surfaces,etc), since books ...
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0answers
15 views

Is semi-lagrangian 1D advection identical to upwind Euler, when $|u|<\Delta x/\Delta t$?

This looked true to me, I worked through the algebra for 1D and confirmed it. But no one seems to mention it, so maybe I'm missing something... I'm using Bridson's SIGGRAPH 2007 course notes. [5MB ...
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33 views

Tips on studying and becoming proficient at vector calculus

I am a computer science undergrad. I am pursuing my second year open university BS mathematics course. I am currently taking a course on Vector calculus. I am using two text-books - Vector analysis by ...
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68 views

Mathematics without coordinate systems

Suppose that a) I understand mathematics to the level of e.g. Rudin's "Principles of mathematical analysis" b) I want to completely expel "coordinate systems" and the resulting "analytic geometry" ...
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16 views

Information about circular sections of an oblique cone with conical base.

I'm looking for information in English about the topic of circular sections of an oblique cone with conical base since almost all the information on this topic is in French and there is little ...
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0answers
16 views

Q: How much overlap is there between pure and applied graduate courses, in the UK?

I am a final year BSc Mathematics student and I am seriously considering taking a Master's sometime soon. Some institutions have two separate courses for pure and applied maths. My question is, if I ...
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1answer
32 views

Determining the values for which a Maclaurin Polynomial approximates $f(x)=\cos(x)$ within an error of 0.001

I'm tasked with determining the values of $x$ for which $f(x)=\cos{x}\approx 1-\frac{x^2}{2!}+\frac{x^4}{4!}$ has an error no greater than 0.001. Using the error for Taylor polynomials $E = |R_n(x)| =...
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0answers
57 views

Background of Commutative Algebra for Cohen-Macaulay orders and bibliography

In this semester, I'm doing a project in Algebra, and I would like take some advices and suggestions. To be more precise, I will study the Cohen-Macaulay Orders and modules in relation to the Krull ...
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0answers
73 views

Is probability heavily related to graph theory?

Can one take a probability elective course without taking any graph theory or advanced combinatorics class before? lets assume that one knows already the basic difference between variation, ...
0
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1answer
72 views

How to get better at simplification?

Related to this question. This problem is the root reason why I was never good at math - I am horrible at all forms of simplification in mathematics, hence I am bad at proofs. The problem is that ...
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61 views

Advice: Which book/topic should I take first: Set Theory or Abstract algebra.

Some background about me. I study on my own and I am not a math major but I am interested in math. I am not even sure if I am mathematically mature enough to handle the 2 topics but I have read a few ...
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0answers
55 views

Motivating undergraduates in learning about the Casimir element

Next week I will give a lecture about a chapter in Lie Algebras (I'm myself an undergraduate student). One of my topics is about the construction of the Casimir element (from Humphreys' book). I'm ...
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0answers
56 views

How to stay mathematically sharp during a engineering gap year

I am on a gap year due to financial reasons but my question is how to stay active during the gap year. I fear that I would lose all the momentum and fail my first year. I will be studying engineering ...
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0answers
211 views

Complex analysis,Functional analysis for deeper understanding Machine Learning.

I want to get deeper into the Machine Learning(theory and application in Finance). I want to ask how relevant are complex analysis and functional analysis as a basis for Machine Learning? Do I need to ...