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votes
9 answers
Why is differential calculus often presented before integral calculus?
Why is differential calculus often presented before integral calculus?
Note: I'm still learning calculus at the moment.
It seems that many elementary calculus texts describe differential calculus before integral calculus. They start with an informal…
user13234
18
votes
4 answers
Emphasizing Statistics instead of Calculus
In a 3 minute talk on ted.com, mathematician Arthur Benjamin made the argument that it makes sense to give emphasis on statistics instead of on calculus in school, after students have been given a basic background on algebra and arithmetic.…
user101
18
votes
2 answers
Tension between the most intuitive definition vs. the most common definition of a concept
Many definitions in mathematics are "fully crystalized". Sometimes the form of these definitions might be somewhat baffling to the uninitiated.
For example, the definition of a relation from $X$ to $Y$ as a subset of $X \times Y$ is extremely…
Steven Gubkin
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18
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4 answers
Does this property of subtraction and division have a name?
Addition and multiplication are commutative. Denoting $\circ$ as either such operation, we have
$$x \circ y = z \Leftrightarrow y \circ x = z.$$
Subtraction and division have a similar property, where
$$x \circ y = z \Leftrightarrow x \circ z =…
Reinstate Monica
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18
votes
4 answers
Online Whiteboard Application with Simple Latex Support
Like a lot of people, my school is in the position of having to move their courses online. Does anyone know a good whiteboard app that allows simple latex entry? The closest I've been able to find is Twiddla
https://www.twiddla.com/t0xq6n
but that…
Nate Bade
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18
votes
7 answers
Lack of intuition, retention while self studying
I am a first year undergraduate student, currently in second semester.
So basically I learnt most of the first year stuff in high school, so I have a lot of free time in this year (currently in second semester), and thus I'm self studying math in…
katana_0
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18
votes
7 answers
Learn university maths or train for high school competitions: which is better?
I sometimes see people arguing against concentrating too many resources in high school maths competition (such as IMO) training. Their reasons they give are usually the following:
Competitions are a very skewed representation of the subject. They…
Ma Joad
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18
votes
8 answers
Should high school teachers say “real numbers” before teaching complex numbers?
Before complex numbers are introduced in senior high school courses, should we emphasise that solutions (e.g. to quadratic equations) are real solutions?
If we do, then when non-real numbers finally arrive, students are (in theory) already somewhat…
lukejanicke
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18
votes
14 answers
What mathematics activities get students physically moving?
What college mathematics topics can be taught in such a way that causes students to physically move around?
Background:
Recently, it was suggested to me by a faculty member (from another academic department) who visited my class that there are…
Nick C
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18
votes
5 answers
What is the most difficult concept to grasp in Calculus 1?
I would say it is not the Fundamental Theorem of Calculus,
but rather some notion connecting limits and continuity,
perhaps the $(\epsilon,\delta)$-definitions of limits and continuity.
But I would be interested to learn from experienced calculus…
Joseph O'Rourke
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18
votes
13 answers
Is there a simple example that empirical evidence is misleading?
Suppose that I want to show a student that empirical evidence in mathematics is not enough and we do need proofs, what kind of examples can I use?
By empirical evidence, I mean that (most of the time) you cannot simply check the statement $S(n)$ for…
user11702
18
votes
5 answers
Rigorous proofs vs. illustrative examples
No one would argue against the idea/ observation that proofs are very important in mathematics. Some people are trying to make their notations on a blackboard during a lecture as consistent as possible with their course notes or textbooks; including…
user35603
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18
votes
10 answers
How to Write Steps of Solving Equations?
This is a common way to write the steps during solving equations:
But in GeoGebra the steps are shown this way (the highlighted part):
I'm going to use GeoGebra to teach equations. Is it OK to let the students write the steps just like GeoGebra (I…
Behzad
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18
votes
1 answer
Is MacLane and Birkoff's "Algebra" suitable today as either an undergraduate or graduate text in abstract algebra?
I'm going to soon review the 3rd edition of Saunders MacLane And Garrett Birkoff's Algebra at my blog soon and this is the first time I'm really carefully reading it. While I'm really enjoying the book,I've got a real dilemma gnawing at me. What…
The Mathemagician
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18
votes
4 answers
How does the workload of a high-school mathematics teacher compare to a university-level instructor?
This question could be very broad, and so I'd like to make it more specific.
In the United States, mathematics educators generally work in secondary education or college education (elementary school specialists exist but are rare).
Secondary…
Brian Rushton
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