In Session 8 we:

• reviewed the division algorithm for numbers
• adapted this to dividing polynomial expressions
• gave a formal definition for a polynomial function
• Exam #1 was returned, see solutions here.

RSA (Rivest, Shamir and Adleman) is a cryptosystem widely used for secure data transmission. In such a cryptosystem, the security of the system is based on the
practical difficulty of factoring the product of two large prime numbers, the factoring problem. For instance, RSA-768, the largest number to be factored to date, had 232 decimal digits and was factored over multiple years ending in 2009, using the equivalent of almost 2000 years of computing on a single 2.2 GHz AMD Opteron processor with 2GB RAM.2! Read more about the RSA crytosystem and the RSA factoring challenge here.

Why should we care?!! The threat of quantum computers to this cryptosystem is real, a quantum algorithm for factoring a 300 decimal digit number needs only 5x 10^10 steps, or with gigahertz speed less than 17 minutes! With a terahertz speed, it takes less than a second! This will force the world to change its infrastructure when it comes to sensitive data transmission. If you want to learn more about quantum computing, read here.

In today’s class we

• covered all of Session #7 in the text
• we worked on the Inverse Functions Worksheet
• WeBWorK problem set on Inverse Functions has been assigned

Read more about Evariste Galois – the father of “Group Theory.”

In Session #5 on 9/12/2017

• Exam #1 was announced for Tuesday 9/19/2017. Topics covered will be from the text: Sessions 1-5. Please remember to bring your graphing calculator and be on time!
• 5.1 Graphing basic functions and 5.2 Basic functions and transformations
• 6.1 Operations on functions given by formulas (addition/subtractions/division)
• Handouts were distributed, Operations on Functions and Graphing and Transformations
• WeBWorK problems sets on Graphs and Transformations and Operations on Functions were assigned

In Session #4 on 9/7/2017 we covered:

• Graphing with the TI-84 calculator
• worked on our WeBWorK problem sets
• if finished, moved on to complete solving the worksheet on graphing

Reminder: We will be working with our graphing calculators today so bring yours to class!

In Session #3 on 9/5/2017 we covered:

• Functions given by formulas, 3.1 and 3.2,
• I assigned a new WeBWorK set: Functional Notation due next Tuesday 9/12/2017
• the WeBWorK problem set on Lines and Graphs is now due next Thursday, 9/14/2017
• I announced Exam #1, which will be on Tuesday 9/19/2017 starting promptly at 8:00 am
• a sample exam will be posted on OpenLab under “Files” on Tuesday 9/12/2017

In class session #2 on 8/31/2017 we covered 2.1 and 2.2

• slopes, intercepts, equations of lines, graphing lines
• introduction to functions
• and did worksheet titled “Lines and Slopes” found in our
• problems #1- #3 can be started from WeBWorK problem set “Lines-Graphs”

In class session #1 we discussed rational and irrational numbers. Specifically, we discussed the irrational number pi. I mentioned the work of two famous number theorists, David and Gregory Chudnovsky and their work on investigating the digits of pi. David and Gregory also happen to be our neighbors – they run the supercomputing lab across the street at NYU Poly (my alma mater). Unfortunately, there is not much recent material about them, but here is an interesting article from the New Yorker about them and their detective work:

http://www.newyorker.com/magazine/1992/03/02/the-mountains-of-pi

Here is the page from Poly’s website:

http://engineering.nyu.edu/chudnovsky