Math 629: History of Mathematics
Frank Sottile

• Opening Remarks: The next week, 13–17 March 2017, is spring break at TAMU. This week is also spring break for my son, so we will take it slowly.
  This week's homework is due Monday, March 20. It is also a little less than before.
  
  
• Reading:
  • Chapters 9 and 10 in Stillwell's book. This covers many of the topics that are taught in the Calculus, as well as quite a lot (in Chapter 10) about formulas involving infinite processes, including infinite sums and infinite products.
  • Look up some sources about logarithms. What were they used for? Who invented them?
    Up until the 1970s logarithms were commonly used as a shortcut to multiplication, because the logarithm turns multiplication (hard) into addition (easy). (For those who have had algebra, this is because the logarithm function is a group isomorphism from the multiplicative group of the positive real numbers to the additive group of the real numbers.)
    When I was a student in high school, they had just stopped teaching logarithms, but they still taught us the tedious task of linearly interpolating values in tables of functions (look that up!) by hand. I also dealt with computer programs on punch cards and walked miles to school uphill both ways.
    Perhaps more interesting is that our perceptions, specifically hearing and sight, are on a logarithmic scale. You might want to think about that as you look up material and do the homework problem on the distribution of data.
• Assignment: Due Monday, March 20. (HW 9) Last week's homework was too hard, so I am trying to be more reasonable this week and in the future.
  To hand in: Email a .pdf to both Bennett Clayton bgclayton@math.tamu.edu and Frank Sottile. fjsteachmath@gmail.com
  1. To help appreciate Stillwell's perspective on the history of the Calculus–that Newton's main contribution was his use and manipulation of power series–do the Exercises 9.5.3 and 9.5.4 and derive his series for sin^-1x. Use Newton's binomial formula for fractional powers.
  2. Everybody loves the Fibonacci sequences (from a problem of Fibonacci about rabbits; it is interesting to look up the source.) Do the three problems in Section 10.6 in Stillwell about this interesting sequence.
  3. I have adapted a project from Prof. Fulling about Benford's law, and the logarithmic scale. Please do the exercise on that page.