Archives for Math - Page 3
Shortest ever Intro to Lie Algebras and Lie Groups
A Lie algebra is simply a) a vector space b) with an "operation" such that the operation of any two vectors x and y is again a vector, and such…
Lie Groups–Notes
Algebraic equations vs. Differential equations Galois Theory – dealt with symmetries in algebraic equations Lie – Tried to do the same (look for underlying symmetries). Lie Groups Are a Group…
Running Sum of Randomly Generated Numbers
Integers from 1 to N are randomly generated . Each integer has an equal probability of being selected and unlimited repetition is permitted. A running sum is maintained. Given any…
Visualizing differential equations
Whenever I read a physics article, I try to visualize the quantities that the author is talking ; I do this by ASSOCIATING the quantity with some REAL thing. Example…
Adventures in teaching–why 5th graders are smarter than grown-ups
A small bag is lying on the ; The room is big – with high ceilings. Yet, no one can jump over the bag. Why? I posed this to several…
Principles versus Laws
People tend to use ‘laws’ interchangeably with ‘principles’. In reality, there is an important difference between the two – as described in this short post. Physics A law encompasses a…
“Deriving” into Pre Calculus, Course S68–S.I.G., University of Texas, Austin
Day 1 - Pre-Assessment Areas of interest, individualized personal objectives Five hardest questions in different areas of calculus Informal class discussion Day 2 - Graphing General equation of a line,…
A probability problem – will these two friends ever meet?
Two friends decide to meet at a definite place between 9 AM and 10 AM. The first to arrive waits for his friend for 15 minutes and then leaves. If…
Modeling Traffic Flow
Traffic flow is not that different from the flow of anything else. Imagine heat flow along an iron rod or water flowing down a pipe. If you observe the traffic…
Complex Transformations – The Complex Logarithmic Function
The real logarithmic function has two interesting properties: The Flattening property: $ \ln(bc) = \ln b + \ln c $ – a product is flattened into a sum The Linearizing…