MA177--How to prepare for the final exam

To help you prepare for the final, here is a list of things you should review. I've tried to cover most of the important things we discussed, and I've also written a few sample essay questions. The exam will have a few short answer questions about concepts and/or people, followed by a couple of essay questions. Feel free to come talk to me at any point if you need help with any of this!

Good luck!

Concepts: You should be able to give a short description of each of the following.

  • The Königsberg bridge problem
  • Scientific academies
  • The Ladies' Diary
  • Newton's Principia
  • Newton's Opticks
  • Universal gravitation
  • Newtonian mechanics
  • Newtonianism on the Continent
  • The problem of the Earth's shape
  • Maupertuis' expedition to Lapland
  • The problem of the vibrating string
  • Leibniz's "principle of continuity"
  • The principle of least action
  • Laplace's Mécanique Céleste
  • Lagrange's Mécanique Analytique
  • "Social choice theory" (elections)
  • "Metaphysics of the Calculus"
  • Fluxion
  • Differential
  • Derivative
  • Berkeley's critique of the Calculus
  • D'Alembert's concept of "limit"
  • The "problem of the points"
  • The Fermat-Pascal letters
  • Probability
  • Expectation
  • Jakob Bernoulli's Ars Conjectandi
  • The St. Petersburg paradox
  • Smallpox inoculation
  • "Probability of judgments"
  • Probabilistic/traditional insurance
  • Number theory
  • Perfect numbers
  • Mersenne primes
  • Pell's equation
  • Fermat's "Little Theorem"
  • Fermat's "Last Theorem"
  • The four squares theorem
  • Primality testing

People: You should be able to describe the mathematical and scientific ideas and/or contributions of the following people. (I don't mean dates and other biographical facts, but you should know some general information about their ideas, their "style," their importance, and their influence.)

  • René Descartes
  • Isaac Newton
  • Gottfried Leibniz
  • Pierre de Fermat
  • Blaise Pascal
  • Jakob Bernoulli
  • Voltaire
  • Émilie du Châtelet
  • Pierre de Maupertuis
  • Alexis Clairaut
  • Leonhard Euler
  • Daniel Bernoulli
  • Denis Diderot
  • Jean-Jacques Rousseau
  • Jean Le Rond D'Alembert
  • Pierre Simon de Laplace
  • Marquis de Condorcet
  • Adrien-Marie Legendre
  • Joseph-Louis Lagrange

Sample Questions: Here are some sample essay questions. You should expect to see similar ones on the exam.



Fernando Q. Gouvea
Wed Dec 3 14:20:07 EST 1997