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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 ...
Dirac Academy of Self Study's user avatar
1 vote
1 answer
382 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 ...
Saravanan's user avatar
  • 123
1 vote
3 answers
189 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 ...
Bach's user avatar
  • 121
1 vote
1 answer
431 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 ...
Merderzo's user avatar
1 vote
1 answer
106 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 ...
user avatar
1 vote
2 answers
156 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 ...
xyzt's user avatar
  • 113
1 vote
1 answer
86 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 ...
Prateek's user avatar
  • 35
1 vote
2 answers
178 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 ...
Abdallah Abusharekh's user avatar
1 vote
1 answer
332 views

Are there differences between graphs, diagrams and charts?

"Can you explain the distinctions between graphs, diagrams, and charts, and provide definitions for each of these concepts? Specifically, is every graph considered a diagram? Are graphs ...
Humberto José Bortolossi's user avatar
1 vote
1 answer
137 views

Pythagoras and Trigonometry sequencing

In teaching the high school curriculum Pythagoras is usually bundled with Trigonometry. They might be justified by way of proof of some sort. They are used to solve 2d and 3d geometry problems for ...
pdmclean's user avatar
  • 967
1 vote
1 answer
226 views

Calculus at competitive level or Olympiad level

What are the topics of Calculus which can be useful for competitive level and the students are not exposed to it ?
πααρτθ Σαρθι's user avatar
1 vote
1 answer
551 views

Best books for mathematical statistics self-study?

I'm hoping to start a masters in mathematics in the fall, and am hoping to find a good book on mathematical statistics to study so that I'll be able to take graduate level mathematical statistics once ...
blakedylanmusic's user avatar
1 vote
1 answer
323 views

Resources to qualify for AIME

I am trying to qualify for AIME this year and get a score of at least $5$ or $6$. (If anyone doesn't know, AIME is the American Invitational Mathematics Examination. You need to get a decent score on ...
I am a person's user avatar
1 vote
2 answers
292 views

Is there a book or Web site that explains how to use and teach the Singapore math block model?

I have been examining sites that illustrate the use of the block model for solving problems. I am an adult with a degree in math and I have an interest in seeing how math can be taught. From what I ...
user1153980's user avatar
1 vote
1 answer
2k views

I'm in 8th grade and just finished Algebra 2. What math would I do for the next 4 years? [closed]

I'm in 8th grade and just finished Algebra 2. What math would I do for the next 2 years? In what order would math I would do in 9th, 10th, 11th, and 12th grade. Thanks!
Luke Justin's user avatar
1 vote
1 answer
109 views

What are some of the struggles that come with teaching introductory formal logic?

I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that ...
Joshua Crotts's user avatar
1 vote
1 answer
289 views

What books are good to study Solid Mensuration?

Preferably I want those that contain the following topics: Solid Figures Polyhedrons Prisms Pyramids Prismatoid Truncated Prisms Cylinders Cones Spheres I've been ...
AndroidV11's user avatar
1 vote
1 answer
60 views

Reference Request: Suitability of a text and corresponding video lecture series request for "Matroid Theory"

I am an undergraduate student from the CS background. While reading a portion of the text "Introduction to Algorithms" by Cormen et. al. I came across a section of Matroids. I was unable to ...
Abhishek Ghosh's user avatar
1 vote
2 answers
261 views

Workbooks for advanced high school math topics

I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them): Logic and sets (propositional calculus, ...
paus's user avatar
  • 83
1 vote
1 answer
195 views

Making epsilon-delta proofs not just precalculus

In trying to find lecture-length videos of epsilon-delta proofs, I've found that almost all of them just start with the definition and then work through the algebra to get the answer. In effect, it ...
user avatar
1 vote
1 answer
111 views

How to use Calculus to give an explanation for a video by Lewin [closed]

In the video by the well-known physicist Water Lewin Link Here, in which he demonstated a series of experiments of rolling objects. Many are quite surprising. At the end of the video, the attended ...
Hana Puk's user avatar
  • 221
1 vote
1 answer
124 views

How to teach geometric patterns? [closed]

I would like to know how to teach geometric patterns in secondary school. I want to elaborate worksheets, which could include different kinds of strategies related to this topic. Are there resources ...
Carlos Torres's user avatar
1 vote
1 answer
526 views

How can I make "complex" graphs that combine multiple functions with a software?

Til today I've been using geogebra to sketch functions for my students quizzes or homework. Sometimes I use the ones that I found searching in google, but this takes a lot of time specially because I ...
Grouper's user avatar
  • 279
1 vote
1 answer
230 views

Evaluation and feedback using Optical Mark Recognition systems in secondary school

OMR in exit tickets I plan to use an OMR, Optical Mark Recognition systems at the end of (some of) my classes. I want to use the same OMR system for exit tickets scattered over the academic year (not ...
Morten Engelsmann's user avatar
1 vote
1 answer
242 views

Can $y^{(n)}$ be used as a way of representing higher order derivatives?

I have never seen this notation, but I think that it follows in a similar vein for function notation. So if $y=f(x)$, then $y''=f''(x)$. Then by that, can we say that $$f^{(n)}(x)=y^{(n)}$$
Eleven-Eleven's user avatar
1 vote
1 answer
136 views

How to build addition with sets?

I was taught under the New Math, so I should know this, but I am afraid I was tricked. Using the cardinal, it is easy to define a multiplication, as the cardinal of the cartesian product is the ...
arivero's user avatar
  • 231
1 vote
4 answers
275 views

The sequence of chapters

I'm using a textbook but in my course the chapters are numbered differently. For example, the book has the following chapters: Real Numbers Square Roots Polynomial in a single variable (they don't ...
user5402's user avatar
  • 1,528
1 vote
1 answer
5k views

Project Based Learning (PBL) ideas for secondary math topics

I have searched the web but not found too much that fits what I want. So, I thought I would try asking here. I am looking for projects to use as PBL for grade 10 math. Specifically for the topics of: ...
mkstreet's user avatar
1 vote
1 answer
176 views

Vector Algebra Text [closed]

Recent developments in Geometric Algebra have extended vector algebra to include the outer product (wedge product) and bivectors. Is there a Vector Algebra text (preferably at the advanced high ...
Allyn Shell's user avatar
1 vote
1 answer
100 views

Math textbook for secondary school using Logo like syntax

What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
paus's user avatar
  • 83
1 vote
2 answers
210 views

Online Probability Simulation for Compound Events

I'm teaching Grade 9 Probability. We need to compare Experiment Probabilities (Relative Frequencies) with Theoretical Probabilities for Simple and Compound Events. I want to come up with and Online ...
pdmclean's user avatar
  • 967
1 vote
1 answer
134 views

Idea of using LLMs to help communicate ideas in math

What do you guys think about the ideas presented in this short text: https://github.com/yougetyourmanwww/AI-for-math/blob/main/AI.md The text is about how LLMs like chatGPT can be used for when doing ...
user23248's user avatar
1 vote
2 answers
164 views

What can be considered as common knowledge in an online Mathematics course?

As I prepare to instruct an online Mathematics course next year, I'm currently writing the syllabus. Right now, I'm writing about student participation in the Learning Management System, which takes ...
throwawayta's user avatar
1 vote
1 answer
432 views

Is there any university or college in any country where failure and dropout rates in Calculus are not so high?

Calculus is a foundational mathematics course that is often seen as a bottleneck for STEM majors. However, it is also a course that is notorious for its high dropout rates. In the United States, for ...
Humberto José Bortolossi's user avatar
1 vote
1 answer
80 views

Discrete Probability Modeling with Desmos or Spreadsheets

In my Finite Math course* almost every section includes a part where students have to create a file (from scratch) in Desmos or in Google Sheets. For example, they use Desmos to plot piecewise linear ...
Aeryk's user avatar
  • 8,019
1 vote
1 answer
77 views

On Teaching Cyclic Groups [closed]

My professor asked me to take 20 mins on talking about Cyclic Groups and their practical applications in front of the whole class. How should I start? Can anyone please help me.
Florence's user avatar
1 vote
1 answer
195 views

Book recommendation for Mathematical olympiads for a +2 student

My Mathematics Olympiads are approaching So I have not started the preparation yet. I need to have a better resource for +2(11th or 12th class basically a high school student) Olympiads so if you have ...
πααρτθ Σαρθι's user avatar
1 vote
1 answer
587 views

Textbooks for Non-Convex Optimization

I’ve studied convex optimization already with Boyd & Vandenberghe's book. Now I need to learn non-convex optimization. What are the best/most common texts for this? Need to learn a general ...
vmusegameon's user avatar
1 vote
1 answer
99 views

Which whiteboard/canvas app with custom background and color options

I'm looking for a PC software whiteboard application that allows for custom RGB background colors and custom RGB pen colors. Most I've seen offer only a handful of color choices for the pen. ...
Ungar Linski's user avatar
1 vote
2 answers
334 views

What books teach the formula for the # of k-permutations of n objects, with x types, and $r_1,⋯,r_x$ = the number of each type of object?

Some of my 16 year old students hanker after the formula for the # of k-permutations of n objects, with x types, where $r_1, ⋯, r_x$ = the number of each type of object. This is more generalized than ...
user avatar
1 vote
1 answer
292 views

The Basic Practice of Statistics vs. Introduction to the Practice of Statistics

How does David S. Moore; William I. Notz; Michael Fligner's 2021 9 edn. The Basic Practice of Statistics differ from David S. Moore; George P. McCabe; Bruce Craig's 2021 10 edn Introduction to the ...
user avatar
1 vote
1 answer
229 views

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...
Abhishek Ghosh's user avatar
1 vote
1 answer
161 views

Resources for Unit Rates

I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
EnlightenedFunky's user avatar
1 vote
2 answers
265 views

Where can I find a good course on tensor calculus not focused on applications and physics?

Where can I find a good course on tensor/ricci calculus not focused on applications and physics? I've been running into lots of tensor-theoretic stuff in differential geometry, so I don't know if ...
John Clever's user avatar
1 vote
1 answer
445 views

Should students get another chance at a math question because of English troubles?

The question is John has locked a 4 digit combination lock with each of the numbers 0-9. He knows the numbers 1,4,6, appears exactly once, but he does not remember the position of the numbers and he ...
Selwyn Liu's user avatar
1 vote
2 answers
222 views

Cautionary tales for Gaussians/the central limit theorem?

In any undergraduate course on probability, one of the fundamental results that is discussed is the central limit theorem. Apart from the interesting mathematics needed to prove the result (most often ...
user78270's user avatar
  • 111
1 vote
1 answer
274 views

Undergraduate Interview Maths Questions [closed]

I am trying to compile a document of preparation questions to use in mock interviews with students applying to study Maths at top UK Universities. I have many questions already, but it is always ...
PhysicsMathsLove's user avatar
1 vote
1 answer
118 views

How to address opportunities for improvement with a teacher

My daughter’s 5th grade teacher gives some pretty impossible questions and I don’t think she understands the material she’s teaching. For example, this question has no context from previous questions ...
Still.Tony's user avatar
1 vote
1 answer
2k views

Motivate your answer vs. Prove your answer

The title is self-explanatory, but what is the appropriate response to "motivate your answer"? Should you prove your answer? Should you just explain it, or give the intuition for it? For example, ...
David J Silverberg's user avatar
1 vote
1 answer
112 views

Verifying Simple Expression Equivalence in a Spreadsheet

For simple expressions with easily derived canonical forms (eg polynomials and simple rational expressions), is there a way to leverage existing tools to verify that two expressions are equal when ...
Zediiiii's user avatar
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