# All Questions

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218 views

### Quadratic equations using complex math but with no imaginary roots

Many years ago when learning complex maths we used complex maths as an example in the quadratic equation to find real roots. My nephew is struggling to deal with complex maths as his teacher is ...
370 views

### When are partial fractions taught? [closed]

Recently I had taken the SATs, and a question came up that involved partial fractions decomposition. $$\frac{x^2-4x+5}{x-3}$$ This is not the exact problem but a similar one. If the SAT math is ...
127 views

### How do I assimilate mathematical concept?

Already knowing that the famous quotation "there is no royal road to mathematics", I believe that the most efficient and best way to learn mathematics is to make it intuitive to oneself, at least to ...
89 views

### Retain problems and combat regression in learning

Regressive Learning It's a really stressful situation. I can achieve but not retain expertise in maths problems. History 6 months back, I studied integration in Calculus at college. I learnt it all ...
321 views

### Is there any age limitation to become a professional mathematician?

Many musicians believe that if one wants to become a professional pianist he/she should begin playing piano when he/she is a child. Question 1: Is this true about mathematics? In other words, is it ...
126 views

### Mnemonics to correlate the definition of “asymmetric relation” and “antisymmetric relation” with the terms [closed]

The definitions from Kenneth Rosen textbook are as : A relation $R$ on a set $A$ such that for all $a,b ∈ A$ ,if $(a,b) ∈ R$ and $(b,a) ∈ R$,then $a=b$ is called antisymmetric. A relation $R$ on a ...
233 views

### How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?

I am teaching math to a 10 year old student. He learned that $$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$ and \frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...
184 views

### How to formulate this type of arcsin problem?

Reading and commenting on What are some common ways students get confused about finding an inverse of a function? I was kindly set straight that the use of $\sin^{^{-1}}(x)$ to mean $\arcsin(x)$ has ...
5k views

### The secret Santa present-swapping paradox [closed]

[This may be the wrong SE for this question. But as a non-mathematician I feel it may be too simple for MathOverflow, and that I might benefit from a school-level explanation. Also, it might make a ...
324 views

### Designing a Good Question on Kinematics: Test and Develop

So I was asked in an interview to design two questions for UK Physics A Level students studying the suvat equations, that is, equations of motion with a constant acceleration. The first needs to '...
222 views

### Solving problems

I have been telling my students to try to solve the problems on their as much as they can. As I tell them, it will help them be better at solving and understanding problems of Mathematics. This thing ...
3k views

### Prerequisites of mathematical analysis [closed]

What topics should I read before studying mathematical analysis? I want to have a solid foundation in terminology, notation and concepts in general. Please suggest titles for books.
249 views

### Are there real life examples of normed vector spaces?

I'm trying to explain some basic concept to my kid (he just started learning basic algebra following Discovering Algebra: An Investigative Approach by Jerald Murdock ). For example homeomorphism means ...
190 views

### Should I do all the proof practice problems in How to Prove It, an intro to proofs book?

Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(...
227 views

### How can I convince authors to publish the Instructor's Solution Manual to students?

This question applies to solely books already accompanied by an ISM ("Instructor's Solution Manual) — access is restricted to instructors. Some don't even sell a SSM (Students' Solution Manual) ...
209 views

### US High School Geometry: What are all the “reasons” allowed in two column proofs?

For a project I am considering on geometry in US high schools, I need a list of all the reasons that are usually allowed in two column geometry proofs there. I have a bachelor's degree in math and ...
226 views

### When are students taught implicit and parametric representations of curves?

Do students learn implicit equations (such as $x^2+y^2-r^2 = 0$) and parametric equations (e.g., $x=a t^2,\;y= 2 a t$) in a first course in algebra, which in the US would be early high school, maybe ...
153 views

### Intuition explanation about Lebesgue measure zero of the rational numbers [closed]

This is a question about the intuition of the rational number having measure zero. Let us consider followng proof: Let $I = [0,1]$ and $Q = \mathbb Q \cap I$ and let $\lambda$ be the Lebesgue measure. ...