# All Questions

3,062 questions
Filter by
Sorted by
Tagged with
2answers
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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\...
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 ...
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 ...
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 '...
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 ...
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.
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 ...
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(...
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) ...
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 ...
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 ...
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. ...
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 ...
1answer
203 views

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\... 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 ... 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 ... 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, ... 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 ... 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 ... 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 ... 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/... 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 ... 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 ... 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 ... 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" ... 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 ... 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? 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? 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 ... 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 ... 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? 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-... 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 ... 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, ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ...

15 30 50 per page