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1500 questions
10
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3 answers
Experiences with online courses, specially MOOC?
Online courses, particularly massive open online courses (MOOC) are the current rage. I can see that having students going through the material presented at their own pace, whenever they have time, and to be able to "rewind" are valuable. But I…
vonbrand
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Term and reference for the problem of students “overassociating” concepts with each other
I am writing a paper directed at a physics-education journal and I want to briefly refer to the phenomenon of students “overassociating” (in lack of a better term) mathematical concepts with each other which have similar notations, names or…
Wrzlprmft
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Why do we need perfect numbers?
Why are perfect numbers important?
What is the best way of introducing these numbers to a first course on number theory?
I could not find any application apart from the relation to Mersenne primes. Are there any other applications of perfect…
user92877
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Textbook for 2nd linear algebra course
I am teaching (for the first time) a 2nd course in linear algebra. The students will have had a beginning course in linear algebra and a beginning course in abstract algebra. I am considering Hoffman and Kunze (which I had in an undergraduate…
Angela
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How can instructors bridge the gap between an engineering course in stochastic systems and a more rigorous Stochastic Processes course?
Systems and electrical engineering graduate students often take a course on stochastic systems (a.k.a. "Probabilistic Systems Analysis"). A typical course will present such topics as multivariable probability distributions, auto- and…
jonsca
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3 answers
The effectiveness of "honors" classes
In many universities there are honors math classes. For example, instead of having five "mixed" Calculus I sections they arrange one "honors" class and four "ordinary" classes.
How effective is this? What are the arguments for and against such…
Maesumi
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10
votes
7 answers
Is it a good idea to give partial points in grading
When grading problems on quizzes and exams, I often break them down into sub-problems, each worth a portion of the total points. I use rubrics to award partial credit for each sub-problem. However, this practice leads to students arguing that their…
user19945
10
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0 answers
Examples for advanced math courses based on measurable learning objectives
Background. I teach math at a German university (both undergraduate courses and courses for Master programmes), mostly for students who major in mathematics or very similar programmes. Students typically choose their major before starting their…
Jochen Glueck
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10
votes
5 answers
Requesting a Polynomial System of Equations
I am teaching a course in commutative algebra, and it includes a project where the students research on a particular topic, solve a small problem and present it to the class.
I usually give my students some project proposals which they can choose…
Aravind Gundakaram
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6 answers
Intuition for order of operations in compound transformations
This is a close cousin of the previous question asked here about transformations inside and outside a function and how they switch things around. I think some of the perspectives there will help here, but I'd also be interested in something specific…
Kevin P. Costello
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How to explain the concept "Without loss of generality" (through examples)?
This is not a precise question. I am curious to know how do you present to your students the (imprecise) concept of "without loss of generality", and how to use it correctly/incorrectly.
I got curious after a student of mine (in calculus $I$), while…
Asaf Shachar
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10
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5 answers
Lowercase vs. uppercase letters for matrix entries
For a matrix $A$ in, say for instance, $\mathbb{R}^{m \times n}$, there are at least two different conventions to denote its entry at position $(j,k)$:
Denote the entry as $a_{jk}$.
Denote the entry as $A_{jk}$ .
In my experience (at several…
Jochen Glueck
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10
votes
3 answers
Failure to distinguish ratios from fractional or percent differences
Consider the following two problems:
(A) Square 2 has sides that are longer than those of square 1 by a factor of 1.1. Compare the areas of the squares.
(B) Square 2 has sides that are longer than those of square 1 by 10%. Compare the areas of the…
user507
10
votes
6 answers
What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?
When I was in late primary and middle school (east coast US, early 1990's), we were assigned a lot of word problems of the following general form:
Mary has eight self-sealing stem bolts. She sells half to John and then finds an additional…
Robert Columbia
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2 answers
Real-world applications of taxicab metric
The taxicab metric can be used to measure distances in idealized gridded cities. However, usually this serves only as a fun exercise for students.
I'm looking for engaging (as non-technical as possible) examples of real-world applications of the…
Paula
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