Questions tagged [education]

For math questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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29 views

Modelling the number of apples an orchard yields with diminishing returns per tree

This is Exercise 7.9 in the University of Washington's precal book. Sylvia has an apple orchard. One season, her 100 trees yielded 140 apples per tree. She wants to increase her production by adding ...
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Using system of linear equations to solve problems

When we have a system of linear equations we are trying to find the solution of the system (if exists). Are we doing the same when we use system of linear equations to describe something (make an ...
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Complex analysis find the laurent series, is my working out correct?

I am posting this on behalf of a friend, she just wants confirmation if her working out is correct. Answer of working out image revised working out answer image Any input is much appreciated Many ...
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1answer
49 views

Simplification conditions for basic expressions

Being somewhat a part-time educator teaching (mostly adults) basic math I find myself troubled by questions I tend to get. Being more specific, students ask me for conditions, algorithms and other ...
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1answer
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Complex Analysis Are My Answers Correct?

Good Evening, I am posting this on behalf of a friend, she has a complex analysis maths exam tomorrow morning and wanted some clarification on her answers however this is not my field, so I am hoping ...
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1answer
84 views

integral of $(x^5+1)\cos(x)$ on a symmetric interval

I gave my Calc II class the following problem on their first assignment of the quarter: $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (x^5+1)\cos x \: dx$, which evaluates to 2 when one takes into account ...
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152 views

Explaining the joy behind Math to the Common Folk [duplicate]

As a math student, it is hard for me to explain the beauty of math to non-mathematicians. So I wonder, how can one explain the elegance of abstract mathematics to somebody without a special background ...
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0answers
37 views

Motivation for the definition of prime and maximal ideals [duplicate]

How do you motivate the concept of a ring-theoretic ideal, and subsequently prime/maximal ideals, to a first-time ring theory student who has never seen these things before? Let's say they just know ...
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48 views

A question about online teaching aids [closed]

Online classes will start again as the semester will start, I bought an XP-Pen deco 03 to help me with online teaching. I will be teaching commutative algebra next semester. I would like to ask what ...
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Reimaging Collimated Beam [migrated]

I am trying to solve a reimaging two lens system and I am aware of the Thin Lens Equation, $ \frac{1}{d_{image}} + \frac{1}{d_{object}} = \frac{1}{f}$ where $f$ is the focal length. My scenario is ...
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1answer
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What does this mathematical expression mean?

I am reading a natural language processing paper and I came across this expression. I don't know what it means. Especially the unif part. $$m_i \sim \operatorname{unif}\{1,n\}\text{ for } i = 1 \text{ ...
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What class order should I use to study calculus? [closed]

I would like to know how I should go about studying calculus, and in what order should I take the classes. I have searched tirelessly for answers and I am still confused. Here is what I have gathered ...
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Reference Request: Symmetry in Chaos

I'm a neuroscience student. Recently I became so interested in the mathematical equations involving order and disorder and the complex plane. I read a book named "Symmetry in chaos" by ...
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Any books similar to Hungerford's Abstract Algebra: An Introduction?

I'm an electrical engineer with the usual math background for engineering (mostly calculus, vector calculus, some DEs, Fourier, some complex analysis, linear algebra). Years ago I picked up a copy of ...
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2answers
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Should we define something after we have prove that exists based on the axioms?

In last days I have a hard time to understand what a definition is in mathematics. Until today I thought definition had a dual role in mathematics. Dictionary role The first role is that it mereley ...
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1answer
38 views

Prove that the following are not inner products.

Show that each of the following (a) <u, v> = u1 v1 + u2 v2; and (b) <u, v> = u1 v2 u3 + v1 u2 v3 is not an inner product on $ℝ^3$, where u = (u1, u2, u3) and v = (v1, v2, v3). A function ...
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1answer
95 views

How to build a strong foundation for university mathematics?

My objective: To study pure mathematics at university level next year. I find Abstract Algebra, Number Theory and Foundations of Maths(Set Theory, FOL, etc.) to be intriguing yet mostly inaccessible ...
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Are higher mathematics exercises mostly about proofs?

Im not a math student and thus I've never studied mathematics at a high level (i just know some calculus, linear algebra and abstract algebra), most of the exercises I've done were all about ...
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1answer
51 views

Are there operations that can't be defined using a rule, and if they exist what is their significance?

Wikipedia:Operations(mathematics) In mathematics, an operation is a function which takes zero or more input values (called operands) to a well-defined output value What I took away from this fact ...
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3answers
36 views

Symbolizing “somebody likes everybody bob likes”

I would like to know how to symbolize "somebody likes everybody bob likes" I have tried the following: for all of x (if bob likes x, then for some y, y likes x) which I think would look like:...
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2answers
44 views

What are some good resources on symmetry?

I find symmetry very appealing so I would politely ask you for some of the best resources (books, courses, articles, etc.) you know on this topic. I would also dare to pose a challenge for the most ...
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How can I find the answer? [duplicate]

Let $a$ and $b$ be two real numbers, and let $c$ be a non-negative real. Show that if |a|≤c and |b|≤c , then $|a+b|+|a−b|≤2c$ Show that if $|a+b|+|a−b|≤2c$, then $|a|≤c$ and $|b|≤c$. Thanks for your ...
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3answers
156 views

Just finished Highschool and I am starting my degree in math after the summer, but in the mean time what subjects should I try and study?

Hi I just finished Highschool, I'm starting a degree in math when the summer is over but I want to do a bit of self-studying just for fun. As you might expect I am not very knowledgeable of college ...
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1answer
90 views

Competitive attitude is devastating my ability to learn mathematics [closed]

I am an undergrad student studying Physics. Although it isn't essential, but I am trying to study the Mathematics syllabus for Math undergrad. I don't really enjoy doing it. But, inside I feel I need ...
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1answer
33 views

How to prove this inequality with some condition?

I have following question. I hope to solve the inequality: $\frac{x^2}2 - x + \frac{x}{\ln(x) -1} < \frac{x^2}2$ in what conditions will be OK? ie, which values for $x$ make the inequality true? ...
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290 views

How does the process of simplifying imaginary numbers actually work?

Sorry in advance if this is a really stupid question In class I've been told that $$\sqrt{-25} = 5j $$ Converting $\sqrt{-25} $ into $5j$ is straightforward for me,...
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K12 Lesson plan

I just have finished my first year teaching math in middle school and I am not satisfied with my work mainly because I think my lesson time organization is inefficient. In my school we are having 90 ...
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1answer
87 views

Why do we need arithmetical operations instead of teaching arithmetic based on the successor function?

Since we can construct the set of natural numbers off of the peano axioms with the operations of addition, subtraction, multiplication and division following, why do we even need 4 arithmetical ...
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2answers
101 views

The essence of the Addition operator within arithmetic

How do I characterize the addition operator, without defining its properties using set theory or the peano axioms, so that someone with special needs could understand and apply it in the context of ...
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1answer
109 views

Short, yet powerful proofs

One of my favorite proofs is the following: Claim: There exists irrational numbers $\alpha$ and $\beta$ such that $\alpha^{\beta}$ is rational. Proof: Let $\alpha = \sqrt{2}^{\sqrt{2}}$ and $\beta = \...
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Is H.L. Royden's REAL ANALYSIS, 4th edition, suitable for these two introductory functional analysis courses?

Is the book Real Analysis by H.L. Royden, 4th edition, suitable for two introductory functional analysis courses comprising the following topics? First Course: Metric spaces: A quick review, ...
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A large part of human learning is visual, is it possible to teach someone who is blind mathematics up to Calc II?

I wanted to post the statistic on how much of learning is visual but those studies aren't backed up well (the studies state approximately 65% of learning is visual). I am asking this question here on ...
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1answer
63 views

What is the probability that a rod broken into three pieces forms a right angled triangle? [closed]

Let the rod be cut at $x$ and $y$. So the three pieces are $x$, $y$ and $l-(x+y)$. What is the probability that the three pieces form a right angled triangle?
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1answer
25 views

Graphic understanding of derivative

I'm about to teach some basics of Math and Phyisics to someone who studied Law and now want to start a Medicine Major. I'm a Phyisics student and I already got some good approaches for every topic, ...
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1answer
37 views

Prove that triangle $\triangle ABC \cong \triangle G H I$ . Explain each step.

My question: Prove that triangle $\triangle ABC \cong \triangle G H I$ . Explain each step. Here are my triangles I proved that $\triangle ABC \cong\triangle DEF$ because the first sign of ...
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1answer
32 views

How do I Find Preparatory Exposure?

I always prefer to be prepared ahead of time, but I am not sure of how to be for a career in mathematics. How do I immerse myself in a formal, mathematical environment without necessarily enrolling in ...
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77 views

Is it a bad idea to use visualizations in studying linear algebra? [closed]

many concepts in linear algebra are explained using visualizations. However, many practical applications of linear algebra use spaces whose dimension is larger than 3 which you cannot visualize. When ...
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1answer
67 views

Best way to spend three months before entering masters program: Review fundamentals, or pre-study topics in the program?

Recently I got an offer letter for a master program (with courses like algebraic topology, algebraic geometry (first chapter of Hartshorne), differential geometry, representation theory, etc... ). Now ...
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44 views

What would be good foundations in order to approach manifolds considering an engineering formation?

I am currently studying control engineering on a sort of graduate level (mostly on my own). However every book on the area mentions certain subjects or areas of mathematics (particularly manifolds and ...
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2answers
111 views

Inconsistent notation for vectors and points in textbooks

Many books on calculus or advanced calculus distinguish between points and vectors. Usually points are denoted by italic letters like $P, Q$, and $R$, and vectors are denoted by bold letters such as $\...
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2answers
633 views

Is it bad to resort to numerical examples to understand the idea behind a proof?

When reading proofs, I often get confused and need to devise my own examples to understand what's going on. Is this practice ok or should I train myself to think in abstract terms? As an example, here'...
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33 views

What could be an example of a convex compact set in $\mathcal{R}^2$

I know what are the conditions for a set to be convex and compact but can't imagine any graphical representation of that, could give some example? I was thinking in an ellipse, since its bounded.
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1answer
39 views

Topology and algebraic topology have any application in biology? [closed]

If so, In what area? evolution, genetecs .... And how good do my computer skills need to be to work in these areas?
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65 views

What are Colleges Using for Math During COVID?

$\textbf{Question:}$ What are colleges using for technology in order to assess students during COVID? I currently use Canvas and I do not feel up to date at all with what I am using. I am wanting to ...
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3answers
25 views

understanding of the number relation for all n, n^3 mod 9 is 0,1, or 8

In the book, Elements of programming CASE ANALYSIS has been listed as one of the approaches to solve a problem. As an example, the book states that for all n , n^3 mod 9 would either be 0,1,8 and even ...
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1answer
53 views

Courses to take during pure math masters to keep data science and applied work as a possibility

I was wondering what courses you can take in a pure math masters to preserve the opportunity to go into data science, economics, policy research or other applied work while preserving the opportunity ...
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14 views

Axial vector of a skew symmetric tensor

What is the relationship between the magnitude of axial vector and the magnitude of its corresponding skew tensor? How can we derive it?
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4answers
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I'm new to Trig and don't understand…

I do not understand how to solve this question. I have searched many websites and have not found any information on how to do it. Find the values for $\theta$ that make each statement true $$\sin(\...
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1answer
24 views

What is the real need and concept of average in normal sense (not in form of calculus)? Please see below what I mean by asking this question.

I know how to calculate average, but never get the idea why we need to do that. For example see a question I did correctly just by following only some steps. I got the correct answer, but don't know ...
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1answer
175 views

How Can I Keep Advancing in Linear Algebra?

I recently graduated with a bachelor's in computer science and a minor in mathematics. Since I won't be enrolled in any more math classes, I want to continue learning and honing my skills by myself. ...

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