Physics and maths of walking a tightrope
Plus article on Nik Wallenda‘s tightrope walk in Chicago.
Category: Blog postings
Carol Dwek
Has a website on Mindset:
In a fixed mindset, people believe their basic qualities, like their intelligence or talent, are simply fixed traits. They spend their time documenting their intelligence or talent instead of developing them. They also believe that talent alone creates success—without effort. They’re wrong.
In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. Virtually all great people have had these qualities.
Teaching a growth mindset creates motivation and productivity in the worlds of business, education, and sports. It enhances relationships. When you read Mindset, you’ll see how.
This is the basic message that I want to get across to all my tutees. Maths can be tamed, and your understanding, and your grade, improved by the right effort.
Her section on Test your Mindset though is a bit disappointing, basically it is the same question asked 16 times. I tried it and came out with a fixed mindset, but I could just have easily responded in such a way as to be informed at the end of the “test” that I had an open mindset. The test is far too simplistic to be of any use.
Optimisation: maxima and minima
Optimisation: some notes and commentary on how to approach these problems, at least as I see them.
Heinemann Higher Mathematics Ex 6Q Question 4:
Mega Menger at the King’s Buildings late October
In Edinburgh the build will be taking place in the James Clerk Maxwell Building, King’s Buildings. Come along to Level 3 between 10am-5pm Monday-Friday (20-24 October) and be part of history! No knowledge of fractals is required, but some practical paper-folding skill will come in handy.
Sets and Functions — the inverse function
Key points:
one-to-one correspondence
Sets and Functions I
This topic will introduce some concepts which are useful for later parts of the course, so again please make a good effort to understand its content. While it could be thought of as a “helper” topic questions on this topic, in its own right, may also occur in the exam.
By the end of this topic you should understand
- what a set is
- what a function or mapping is
- what the domain of a function is
- what the range of a function is
- what a composite function is
- that f(g(x)) != g(f(x)) in general [!= means “not equal to”]
- one-to-one correspondence
- about the inverse function
- the effect of applying a function and then its inverse
- the graph of the inverse function is found by reflecting the graph of the function in the line y = x
- about exponential functions to a given base a
- about logarithmic functions to a given base a
The content of this topic is more abstract than the rest of the course but it will make topics to be encountered later on that are difficult, much easier to understand, and so this topic should not be dismissed as unimportant, or as a standalone topic.
The straight line II
The straight line I
By the end of this topic you should be able to answer the following questions
- Can you calculate the gradient of the line connecting two points eg (4,2) and (-5,7)?
- Positive lines slope in which direction?
- Negative lines slope in which direction?
- What is the gradient of a line parallel to the x-axis?
- What is the gradient of a line parallel to the y-axis?
- What can you say about the gradients of lines which are parallel to each other?
- How are the gradient of a line and the angle it makes in the positive direction of the x-axis related?
- How are the gradients of perpendicular lines related?
The knowledge and methods used in this topic occur in later topics so please make the effort to master them.
Fermi estimation
How good are you at estimating? Do you agree that it is a skill worth acquiring?
Plus magazine article on The art of guessing