Articles of soft question

Is 'no solution' the same as 'undefined'?

Today in class my teacher wrote something along the lines of: $6^x = 0$ And proceed to heed a response from the class. A few people shouted undefined. So the teacher then writes: no solution $\therefore$ undefined Now my question: Is undefined the same thing as no solution? From what i understand about ‘undefined’ is […]

A continued fraction for $\sqrt{2}\Bigg({e^\sqrt{2}-1 \above 1.5pt e^\sqrt{2}+1 }\Bigg)$

This question is about the integer sequence A123168. The title of the sequence reads: Continued fraction for – $$\sqrt{2}\Bigg({e^\sqrt{2}-1 \above 1.5pt e^\sqrt{2}+1 }\Bigg)$$ A comment claims that ‘this continued fraction shows that $e^\sqrt{2}$ is irrational”. I thought Lindemann & Weierstrass theorem established the irrationality of $e^\sqrt{2}$ so what is the motivation behind this particular continued […]

Help in self-studying mathematics.

Is this a reasonable list for who seek to learn mathematics by “self learning” program? and is it a well sorted list to follow? http://www.math.niu.edu/~rusin/known-math/index/index.html

What does “rigor” mean in mathematics?

This question already has an answer here: what exactly is mathematical rigor? 1 answer

Analogy of ideals with Normal subgroups in groups.

I’ve started with Ideals in ring theory but still not comfortable with the analogy it has with normal subgroups in group theory.Like we can visualize normal subgroups as Is there some good intutive way to visualize Ideals to see the analogy?

Book to prepare for university math?

Can you suggest some books to prepare for university math?

What is the exact motivation for the Minkowski metric?

In introductory texts about Lorentz Geometry, one always learns about the Minkowski space, i.e. $R^4$ with the Minkowski metric $$ m(x, y) := -x_0 y_0 + x_1y_1 + x_2y_2+ x_3 y_3 $$ Using this metric, one can define lightcones $\{x \in R^4 \mid m(x, x) = 0 \}$ and timecones $\{x \in R^4 \mid m(x, […]

Examples of useful Category theory results?

I’m layman to Category theory. Trying to understand it, I just read a bit briefing on it and wiki pages of Category, Functor, Morphism. However I still could not see the merits of it. Category theory, in layman’s eyes, is another layer of abstract, similar to abstract algebra’s group, ring, field or set theory’s induction, […]

Reference request: calculus of variations

I am searching for a good book to self-study calculus of variations. It should be fairly complete; build up gradually from the very basics; offer detailed explanations; have some emphasis on applications of variational methods.

Map of Mathematical Logic

My undergraduate University does not offer advanced courses on logic, I know truth tables, Boolean algebra, propositional calculus. However I want to pursue Mathematical Logic on the long term as a mathematician. Can anyone suggest a study-map of Mathematical Logic. such as (1) Learn The following topics : a,b,c,etc.. (2) once you learned topics in […]