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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 ...
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1answer
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 ...
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2answers
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 ...
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2answers
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 ...
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3answers
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 ...
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1answer
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 ...
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2answers
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\...
1
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1answer
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 ...
1
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3answers
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 ...
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2answers
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 '...
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2answers
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 ...
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4answers
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.
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1answer
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 ...
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2answers
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(...
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2answers
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) ...
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1answer
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 ...
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3answers
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 ...
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1answer
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. ...
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2answers
214 views

Are books as old as J.E. Thompson's “for the practical man” series outdated?

I'm sure Thompson's books were a fine series back in his time, but are they still worth recommending for, say, interested high-school students or prospective college students that want to brush up ...
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1answer
203 views

What to call a symbol that denotes an “undisclosed” given number? [closed]

Students like to categorize notations to pin down their understanding of exactly what these notations stand for. Thus, given the expressions $f(x_{0})=f(x)|_{x\leftarrow x_{0}}$, $x=x_0+h$, or $lim_{x\...
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2answers
155 views

Topics for undergraduate seminar for mathematics educators

There are some general questions about potential topics for undergraduate seminars: topics for an undergraduate Math seminar Undergraduate Math Seminar topic I am looking for topics for a 15-hour ...
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1answer
153 views

Math undergrad courses [closed]

Awhile back I was very weak with my trigonometry so I came to this site asking for help, and it turned out the few answers I got made a huge difference. I excelled at the trigonometry section in my ...
1
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1answer
126 views

Roadmap to studying PDEs for analyzing Quantum Physics better

I am studying the basics of Quantum Physics (involving the characteristics of Schrodinger's Wave equation without actually analyzing it rigorously mathematically) this semester. I was wondering, ...
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2answers
153 views

Activities for calc based physics

I was sort of thrown into teaching calculus based physics to a bunch of non-physics majors, who have taken one semester of calculus, and are poor with that material. It is only a 50 minute per week ...
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2answers
108 views

Subject advice in Number Theory [closed]

At my University, we have the optional feature to write a project like a Bachelor Thesis. This semester have finished and I would like to work in the summer in project like this. So, I'm searching for ...
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2answers
144 views

AB 86 Basic Skills Mathematics Courses at the Community College Level [closed]

I am a basic skills community college math instructor here in Los Angeles. This Spring is a very exciting time for our college. There are several campus initiatives taking place. Among them is the ...
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1answer
108 views

Advice for a starting teacher [closed]

If you were starting to teach now (as I am), what advice you wish you had gotten? Things as: hopes you wish you did/didn't have specific knowledge you wish you were more knowledgeable books/...
1
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1answer
79 views

Hourly math contests online

You can play chess online anytime you want to, even against a human opponent of your level, even in hourly competitions. It would be nice to have the same thing in math, at least for kids. Everyone ...
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1answer
123 views

How to create an online examination in a small class that ensures certain academic integrity

I am teaching a Calculus class with around 30 students. The classroom is about 100 m^2. So far I have been using myopenmath.com to assign homework problems to my students. Now I would like to deliver ...
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1answer
97 views

asynchronous teaching and requiring frequent email updates from students, and having these as the only part of their grade

Due to the COVID pandemic, classes at my school (small public liberal arts college) will be all online. I've chosen to try teaching asynchronously (via pre-made video lectures) starting next week. I ...
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2answers
275 views

Interpretation of how to define “bigger” and “smaller” real numbers

This is a variant on the question small real numbers. I have a disagreement with someone about the meaning of "bigger" real numbers. Say we have the real number $-1.$ Is $0$ "bigger" or "smaller" ...
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4answers
210 views

Analogy for nested loops/integrals

In teaching students how to do iterated integrals, I would like to find some analogy using a finite task nested inside another finite task. It would be especially nice if it satisfied the following ...
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1answer
242 views

When self teaching, should I learn set theory before continuing ap calculus?

I am studying ap calculus now, before I move onto differential equations etc., but the thing I am unsure of is, should I learn set theory before continuing on my ap calculus sections?
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2answers
129 views

Complex numbers [closed]

I would like to learn the subject 'complex numbers'. My goal is to study this on my own. Are there any good tips, books, sites to study this?
1
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1answer
396 views

How to take notes when teacher uses slides?

I am having trouble with taking notes in class. I believe this is because we are using slides for the course. Slides bombard students with all this information, and at the same time the teacher is ...
1
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3answers
240 views

How to tell the Axioms from the Assumptions

Are there criteria, that allow one to decide, whether something, which isn't a consquence of a theorie's axioms, but is exploitet in a proof, is a further axiom and not an assumption? A concrete ...
1
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1answer
276 views

Honors Precalculus: what topics to cut?

We’re precalculus honors teachers. In this year of Covid and reduced instructional time, what topics can we cut (Demana textbook) that would not hurt our kids in either calc AB or BC?
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2answers
152 views

How to summarize textbook material?

I'm taking a discrete math course. The textbook we use is such a pain to read because the amount of material is very overwhelming. For example, chapter 1 alone is 115 pages. And every subsection, 1.1-...
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1answer
100 views

Questions relating to inclusion-exclusion principle [closed]

Today I came across the inclusion-exclusion principle for the first time. I believe I have understood it, however when I tried solving some questions on it, I got severely stuck. I couldn't solve any ...
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1answer
179 views

Which Geometry book is more rigorous/harder?

Can anyone please tell me if the AOPS (Art of Problem Solving) Geometry is more rigorous/difficult generally than a book called "Geometry for Enjoyment and Challenge" by authors Rhoad, ...
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2answers
156 views

What are the resources to learn prerequisite knowledge to latter High school and undergrad prep textbooks?

I use textbook study and am planning on studying Spivak's Calculus, Mathematics It's Content, Methods, and Meaning, How to Prove it by Velleman, etc. However, I'm worried I lack the prerequisite ...
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1answer
210 views

How to improve mathematical skills(University level)?

I am doing Ph.D in Mathematics, I feel I lack few of the skills, if I can improve those skills I think I can do better as a Math scholar. I need some suggestion on these following(below I am talking ...
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3answers
127 views

How can I measure the mathematical computation skills of high school students through a test?

How to analyze the level of difficulty of mathematical computation of a problem on a standard mathematical test designed for high school students? I mean how to choose some indices that can reflect ...
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2answers
293 views

Line Integral Motivation

Is there a case to be made that the topic of line integrals should only involve vector fields? My colleagues and our textbook take the position that line integrals should only be taught from a vector ...
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1answer
264 views

How can I introduce a speech about the Fibonacci sequence creativiely?

I am a high school senior student. Soon, I am giving a presentation about the Fibonacci sequence and I am searching for a creative way to start my speech. I was wondering whether someone in this ...
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1answer
99 views

Does studying elementary number theory improve one's proof skills and ability to understand algebra and analysis? [closed]

I'm taking a number theory course and don't know whether it's worth it. I currently can't understand algebra and real analysis and decided to take # theory to see whether this would help me prove and ...
1
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2answers
134 views

Interesting math lesson on integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs

I have to deliver a lecture for secondary school, about one of these topics: integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs. It should ...
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1answer
169 views

Math Scholarships for the highly advanced

I was wondering if there are any special math scholarships in the United States of America for High School students with high capacity in mathematics. At the age of merely 16, I see great potential ...
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1answer
83 views

In which order should I read these topics? [closed]

In which order should these topic be read if one have to understand mathematics topic well? Differential Equations Game Theory Graph Theory Linear Programming Probability Statistics Vector ...
1
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2answers
144 views

How to preserve axioms from the positive numbers in the negative numbers?

It isn't so hard to convince students of grade 8. 9 that $-2$ is greater than $-4$, but it still make some confusion with an axiom says that ( The whole is greater than part ), which is true in the ...

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