The Math Major

CSU Fresno Mathematics Department

Vol 2. No. 13

Editor: Dr. Larry Cusick.

Math Department Colloquia

• Date: Thursday, April 30, 4:10 pm
• Speaker: Dr. Eleanor Rieffel, Fuji-Xerox Palo Alto Laboratory
• Title: How to Compute with Schroedinger's Cat
• Location: Science 143
• Abstract:In the early 1970's, Richard Feynman observed that certain quantum mechanical effects could not be simulated efficiently on a computer. This observation led to speculation that perhaps computation in general could be done more efficiently if it made use of quantum effects. But building computational machines, quantum computers, that used quantum mechanical effects proved tricky, and as no one was sure how to use quantum effects to speed up computation, the field developed slowly.

  It wasn't until 1994, when Peter Shor surprised the world by describing a polynomial time quantum algorithm for factoring integers, that the field of quantum computing came into its own. It was so widely believed that no fast algorithm for factoring integers existed that many cryptography systems use the difficulty of factoring integers as the basis of their security. Peter Shor's work prompted a flurry of activity, both among experimentalists trying to build quantum computers and theoreticians trying to find other quantum algorithms.

  This field is in its infancy, and its language is the language of mathematics, particularly linear algebra. The talk will begin with a discussion of basic quantum mechanics, including a live demo of quantum effects. Quantum computation will then be described, with particular emphasis on how quantum computers can be programmed and where their power comes from.

Math Club Film Series

• Date: Tuesday, April 28, 5 pm
• Film: "Courant in Gottingen and New York"
• Location: PB 428
• Description:
  
  Richard Courant (1888-1972)

  Richard Courant obtained his doctorate from Gottingen in 1910 under David Hilbert's supervision. He taught mathematics at Gottingen, where he was Felix Klein's successor, until the start of World War I. A few years after the war, Courant returned to Gottingen, where he founded the university's Mathematics Institute. From 1920 until 1933 he was director of the Mathematics Institute.

  His most important work was in mathematical physics. In 1924 he published, jointly with Hilbert, an important text Methoden der Mathematischen Physik. He left for England in 1933, going to New York University the following year. He built up an applied mathematics research center in New York based on the Gottingen style. (From the MacTutor History of Mathematics archive)

Seventeenth CSU, Fresno Math Field Day: A Success

A Mathematical Quote

-- Sir William Rowan Hamilton (1805-1865)

Problem Corner

Problem 2.12: Prove that if a, b and c are distinct (no two the same) positive real numbers then a³ + b³ + c³> 3 abc.

Solution to Problem 2.12: Since a and b are unequal, (a-b)² > 0, and so after expanding and rearranging gives a² + b² > 2 ab. Similarly, b² + c² > 2 b c. Adding and dividing by 2, a² + b² + c² > ab + bc + ac. Multiplying both terms of the inequality by a+b + c, and omitting the terms common to both, we have a³ + b³ + c³ > 3abc.

There was only one solution turned in, and it was incorrect.

New Problem

Solutions may be delivered to the math department office (for Dr. Cusick) or by e-mail at larryc@csufresno.edu. There is a $75 dollar first prize and a $50 second prize to be awarded at the end of the semester to the student(s) who submit the most correct solutions.