Questions about studying mathematics without formal instruction.
4
votes
2answers
145 views
Going back to the basics?
I'm currently in my second year of college majoring in comp sci and I haven't really taken any math courses yet except pre-calc. In high school, I thought of myself as a pretty good math student and ...
1
vote
1answer
27 views
Good introductory book for self-studying quasigroups?
I'm looking for an undergraduate or beginning graduate level text from which to self-learn quasigroup theory. An emphasis on using quasigroups to understand the structure of groups would be ...
0
votes
3answers
66 views
Which is true $A$ is subset of $B$ or $B$ is subset of $A$.
Consider the sets dened by the real solutions of the inequalities $$A=\{(x,y):x^2+y^4\le 1\}$$ and $$B=\{(x,y):x^4+y^6\le 1\}$$Then which is true $A$ is subset of $B$ or $B$ is subset of $A$.
...
3
votes
1answer
40 views
14
votes
1answer
220 views
Why learning modern algebraic geometry is so complicated?
Many students - myself included - have a lot of problems in learning scheme theory. I don't think that the obstacle is the extreme abstraction of the subject, on the contrary, this is really the ...
3
votes
2answers
55 views
How to show that there does not exist any integer $b$ with $f(b)=14.$
Let $f(x)$ be a polynomial with integer coefficients. Suppose that there exist distinct integers $a_1,a_2,a_3,a_4,$ such that $f(a_1)=f(a_2)=f(a_3)=f(a_4)=3.$ Then show that there does not exist ...
6
votes
3answers
106 views
How can I find all the solutions of $\sin^5x+\cos^3x=1$
Find all the solutions of $$\sin^5x+\cos^3x=1$$
Trial:$x=0$ is a solution of this equation. How can I find other solutions (if any). Please help.
7
votes
2answers
52 views
How to show this inequality?
Show that $$-2 \le \cos \theta(\sin \theta+\sqrt{\sin^2 \theta +3})\le2$$
Trial: I know that $-\dfrac 1 2 \le \cos \theta\cdot\sin \theta \le \dfrac 1 2$ and $\sqrt 3\le\sqrt{\sin^2 \theta ...
5
votes
3answers
109 views
Importance of Neatness / Organization / Speed in Math?
Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes.
How important is neatness in math?
Does having messy writing put ...
7
votes
1answer
127 views
How to improve mathematical creativity?
To introduce myself: I'm an undergraduate mathematics student in Germany. Currently I'm studying in the second semester and until now I'm doing well, but I still got the feeling that my ability to ...
2
votes
1answer
47 views
Helpful to review certain calculus topics before first real analysis course?
This is my first time posting, so I apologize in advance if my question is inappropriate here. I wanted to know if it would be beneficial for me to review certain calculus topics before I take my ...
2
votes
1answer
35 views
Expected value of function of negative binomial
With $X$ representing the total number of trials, and m the fixed number of successes. The pdf is then
$f(x|p)=$${x-1}\choose{m-1}$$p^m (1-p)^{x-m} \ \ \ \ x \ge m$
As a step in something else I'm ...
11
votes
2answers
246 views
Math blogs, pros and cons for writers?
I regularly read blogs by three mathematicians, and occasionally run into others. Definitely they help me a lot studying mathematics.
But now I am more interested in the writers' perspective, and I ...
2
votes
1answer
46 views
getting started self study
I am 14 and currently in year 10 (uk). I am very interested in maths and intend to pursue it. I currently can do C1, C2, C3 and parts of C4 edexcel exam board a level mathematics. However, when i ...
7
votes
2answers
183 views
What kind of math topics exist?
What kind of math topics exist?
The question says everything I want to know, but for more details: I enjoy studying mathematics but the problem is that I can't find any information with a summary ...
0
votes
0answers
14 views
Joint distribution function of $X$(discrete) and $Y$(continuous)
Let the probability density function of $(Y_1, \ldots, Y_k)$ be a Dirichlet distribution parameterized by $\alpha_1 , \ldots, \alpha_k$, that is
$$
f(y_1, \ldots, y_k|\alpha_1, \ldots, \alpha_k) = ...
2
votes
1answer
80 views
Can somebody provide an explanation to the formula of a one elementary integral?
Here is the formula:
$$
\int{\frac{dx}{x}} = \ln{|x|} + C
$$
In my textbook it is given without proof, so I have a little confusion here. From the definition of integral this equality must be true:
...
5
votes
4answers
128 views
Arithmetic mean is less than geometric mean (Spivak Calculus 3rd Chapter 2 Problem 22)
If $a_1, \ldots, a_n \ge 0$, the arithmetic mean $$A_n={a_1 + \cdots + a_n \over n}$$ and the geometric mean $$G_n = \sqrt[n]{a_1 \cdots a_n}$$ satisfy $G_n \le A_n$.
As a first step to prove this ...
2
votes
1answer
33 views
When in topology is $A = f^{-1} \circ f[A]$ or $B = f \circ f^{-1}[B]$ true, for an $f$ which is not one-to-one?
I'm having a bit of trouble with an example problem in the topology book I'm reading. It's problem #11 (pp 104) of the "Solved Problems" section of Chapter 7, of the Schaum's Outline for "General ...
2
votes
2answers
68 views
learning/teaching approach to rigorous math with the goal of improving
I will state this now: yes, this is a subjective question. But I feel the answers people give may benefit students.
I want to get better at doing non trivial proofs. Real analysis is standard ...
0
votes
3answers
48 views
Given a line segment. Construct an equilateral triangle with one side the given line segment.
I found this problem in a website, but I don't know how to solve it.
Given a line segment $AB$. Construct an equilateral triangle with one side being $AB$.
5
votes
2answers
112 views
Is there a correct order to learning maths properly?
I am a high school student but I would like to self-learn higher level maths so is there a correct order to do that?
I have learnt pre-calculus, calculus, algebra, series and sequences, combinatorics, ...
4
votes
4answers
92 views
Learning trigonometry on my own.
I have been self teaching myself math beginning with a grade 10 level for a while now and need learn trigonometry from near scratch.
I am seeking both books and perhaps lectures on trigonometry and ...
3
votes
1answer
115 views
Self-learning; Physics and Mathematics
My fields of interest are Physics and Mathematics. Gerard t'Hooft, 1999 Physics Noble Prize Laureate, has suggested a better scheme to study physics online. I can't wait for the university, so I've ...
5
votes
0answers
90 views
Where do I go from Linear algebra past Calc III to try to learn complex physics (relativity and quantum group theory)?
I'm mainly a programmer, but I have a love for Mathematics that's been, well, insatiable. I've had my eye on learning Quantum Groups and Relativity, but I want to stay in something I can do with ...
1
vote
2answers
86 views
The maths required for an economics degree
I have a degree in computer science and I wanted to do another degree in economics.
However, my maths have been weak since high school always scoring slightly above passing rate. During my course of ...
2
votes
1answer
128 views
Looking for a math study/project-mate
I'm a math major and was wondering what to do over this summer, since I'm not going for any internships/have any fixated family agenda. I was thinking of working out a book, like Spivak, or work on a ...
4
votes
2answers
130 views
In what order should mathematical fields be learned? [closed]
This could be considered a broader version of this question, with all fields.
I know that when high-level maths are reached, the fields being to split quickly (i.e. specializing in this type of ...
3
votes
3answers
88 views
What math will I need in order to learn Microsoft's UProve?
I'm studying Microsoft's UProve (independent studies at 35 years old) and forget most of the Math I learned in college.
I intend to proceed and learn the contents of this chapter of this book but can ...
6
votes
0answers
104 views
Advice on learning mathematics
I know it is hard to ask for the perfect method for doing mathematics, but I hope there are some paths that are more preferable over others. I am a engineering student who has switched to mathematics ...
2
votes
1answer
81 views
Application of Runge's theorem
Runge's theorem states:
Let $K$ be a compact subset of $\mathbb C$ and let $S\subset \overline{\mathbb C}\setminus K$, such that $S$ contains at least one
point in each connected component of ...
0
votes
2answers
65 views
Expecting a Discontinuity in Piecewise Function on TI-89 but finding Unexpected Results
When I look at the following function $f(x)$, it would seem to me that because there are no $\le$ or $\ge$ inequalities included where the function's formula changes (for the parts relating to ...
4
votes
0answers
53 views
What are the prerequisites for stochastic calculus?
I am not a math student, and only kind of picking up something whenever I need it. After emerged in the field of machine learning, probability, measure theory and functional analysis seem to be quite ...
6
votes
4answers
178 views
Beyond the Exercises? [closed]
I've entertained and become bored with quite a few interests, though mathematics has more or less been my central passion throughout my high school/middle school life. I've only recently started into ...
5
votes
3answers
153 views
How to fill gaps in my math knowledge?
Just finishing highschool, even though I am doing "well" (in the context of the math course itself), I have significant holes in my actual math knowledge.
As I think many people who explore math ...
1
vote
3answers
107 views
Is there a problem in studying analysis before calculus? [closed]
Is there a problem in studying analysis before calculus? Most people say that analysis is rigorous calculus, the university I'm studying teaches calculus first because they believe it's better for the ...
3
votes
3answers
129 views
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
I have been having a lot of trouble teaching myself rings, so much so that even "simple" proofs are really difficult for me. I think I am finally starting to get it, but just to be sure could some one ...
10
votes
8answers
409 views
Suggest an Antique Math Book worth reading?
I'm not a math wizard, but I recently started reading through a few math books to prepare myself for some upcoming classes and I'm starting to really get into it. Then I noticed a few antique math ...
0
votes
2answers
142 views
If $p_1 = 0.3$ and $p_2 = 0.4$, what is the probability that it will take Jay more than 12 hours to be successful on both jobs?
Jay has two jobs to do, one after the other. Each attempt at job $i$ takes one hour and is successful with probability $p_i$. If $p_1 = 0.3$ and $p_2 = 0.4$, what is the probability that it will take ...
1
vote
4answers
36 views
Measure nonzero implies dense on a rectangle
This would be a very handy lemma for me but I have been unable to prove it thus far.
If $S \in \mathbb{R}^n$ is bounded and is not of measure zero, then there exists a rectangle $R$ such that $S$ ...
3
votes
2answers
252 views
An ambulance problem involve sum of two independent uniform random variables
An ambulance travels back and forth at a constant speed along a road of length $L$. At a certain moment of time, an accident occurs at a point uniformly distributed on the road.[That is, the distance ...
2
votes
1answer
81 views
How does one study with many textbooks?
Suppose you wanted a good understanding of a subject, and so you start reading a recommended textbook. But it turns out that the textbook you have has a different perspective/omits certain topics, ...
9
votes
3answers
191 views
Being ready to study calculus
Some background: I have a degree in computer science, but the math was limited and this was 10 years ago. High school was way before that. A year ago I relearnt algebra (factoring, solving linear ...
0
votes
3answers
42 views
Independent random variables $Y_i$ with $Y_i \sim N(0,\sigma^2)$
I am struggeling with this problem:
How to show that, $E(Y^2 _i /σ^2) = 1$
I tried:
$$E(Y^2 _i /σ^2)=E(Y^2 _i /(Y_i - \bar{Y})^2) = E(Y^2 _i /(Y^2 _i - 2Y_i\bar{Y} + \bar{Y}))=...$$
However, I am ...
1
vote
1answer
166 views
What's the best way to measure mathematical ability?
Very soft question I admit, but it's something that's been bothering me for a while.
I've been thinking that being self taught has the problem of accreditation. You can't evaluate a mathematician ...
1
vote
2answers
106 views
How to effectively calculate $(1/\sqrt1 + \sqrt2) + (1/\sqrt2 + \sqrt3) +\cdots + (1/\sqrt{99} + \sqrt{100})$ [duplicate]
I have this series:
$$\frac{1}{\sqrt1 + \sqrt2} +\frac{1}{\sqrt2 + \sqrt3} +\frac{1}{\sqrt3 + \sqrt4} +\cdots+\frac{1}{\sqrt{99} + \sqrt{100}} $$
My question is, what approach would you use to ...
1
vote
3answers
197 views
What are the best websites for learning math? [closed]
What I known:
this site
mathoverflow
khanacademy
Are there any other website for learning math? Which one do you think is the best?
1
vote
1answer
88 views
The shape of mathematical self-tutelage
I am interested primarily in physics, and I am generally self-taught in mathematics. However, this implies an inaptitude for rigorous proof. While I am confident that I can grasp the concepts and ...
1
vote
1answer
87 views
How much time should one devote to solving exercises? [closed]
My question is about learning introductory real analysis at undergraduate level. How much time should I allocate to each exercise before looking at solutions? If I give too much time I can never keep ...
1
vote
1answer
92 views
Selecting Differential Geometry Exercises
I'm self-studying differential geometry with Do Carmo's books "Differential Geometry of Curves and Surfaces" and "Riemannian Geometry" and I find those books very good, however I feel a little ...
