Assignments

**Thu., May. 8:****Final Examination:**4:00 – 6:00**Blog of last minute questions**(PDF for printing —classical HTML for terminal window browsing)

**Note:**this page may have changed since the last time you looked at it. Therefore,**reload**it each time you look at it.**Wed., May. 7:****Office hours:**3:00 – 5:00**Tue., May. 6:**- Last regular class meeting.
**Bring questions**for review. **Thu., May. 1:****Written Assignment No. 5**(PDF for printing —classical HTML for terminal window browsing) is due.**Tue., April. 29:**Convert the word “sage” to its vector of ASCII codes and then use El Gamal encryption for multiplicative arithmetic modulo the prime 257 to encrypt these values using the formula

x :--> [b^{k}, x · c^{k}] (mod 257) where b = 102 and c = 150 employing for the 4 characters the 4 successive values k = 11, 12, 13, 14.

How can the word “sage” be recovered from the four pairs of values modulo 257 that were obtained in the preceding exercise?

A message is waiting for you at the url

The El Gamal key for decoding it as 950. What is the content of the message?`http://math.albany.edu/~hammond/maple/pvc`.

*Added after the class:*Solution of Exercise 3 (PDF for printing —classical HTML for terminal window browsing).**Thu., April. 24:**- Do these these exercises (PDF for printing —classical HTML for terminal window browsing).
**Tues., Apr. 22:****Read:**§§ 10.5, 10.6**Thu., April. 17:****Written Assignment No. 4**(PDF for printing —classical HTML for terminal window browsing) is due.**Tue., April. 15:**-
Become familiar with the functions for cubic curves found at the course's code archive,

`http://www.albany.edu/~hammond/maple/`.Use this introduction (PDF for printing —classical HTML for terminal window browsing) as a beginning guide.

**Thu., April. 10:**- Study the slides (also available as PDF or DVI or classical HTML) about addition of points on cubic curves.
**Tue., Apr. 8:****Read:**§§ 10.1 – 10.2**Thu., Apr. 3:****Written Assignment No. 3**(PDF for printing —classical HTML for terminal window browsing) is due.**Tue., Apr. 1:****Read:**§§ 9.1 – 9.2**Tue., Thu., Mar. 25, 27:****No classes:**university recess.**Thu., Mar. 20:****Read:**§§ 7.4 – 7.6, 8.6 – 8.8Do these:

**188:**3, 4, 5Explore the

*Maple*function for finding primitive roots mod m, which is`numtheory[primroot]`.Let p be the prime 128^{15} + 39. Without trying to solve determine which of the following two congruence equations is solvable:

2^{m} **EQUIV**11 (mod p) ਊnd 11^{n}**EQUIV**2 (mod p) .Are you able to solve the solvable one?

**Tue., Mar. 18:****Read:**§§ 7.1 – 7.3**Thu., Mar. 13:****Read:**§§ 6.1 – 6.3**Tue., Mar. 11:****Midterm Test**(in class)**Thu., Mar. 6:**- Bring
**review questions**

**Read:**§§ 5.3 – 5.4 **Tue., Mar. 4:****Written Assignment No. 2**(PDF for printing —classical HTML for terminal window browsing) is due.

Code for vector shifting of the type used in problem 5 may be found at`http://www.albany.edu/~hammond/maple/`.**Thu., Feb. 28:****Read:**§§ 5.1 – 5.2**Tue., Feb. 26:****Announcement:**The midterm test will be held on Tuesday, March 11.

**Scan:**Chapter 4

**Exercises:****Thu., Feb. 21:****Read:**§§ 8.1 – 8.4

**Exercises:**Study the formulas and do the exercise found in this web page (PDF for printing —classical HTML for terminal window browsing).

What rational number is represented in base 8 by the vector triple

(u, v, w) = ([2], [1], [1, 5, 4, 6, 6, 3, 3]) ?

**Tue., Feb. 19:****No class;**the University will be in recess.**Thu., Feb. 14:****Read:**§§ 3.4 – 3.6

**Exercises:****Tue., Feb. 12:****Written Assignment No. 1**(PDF for printing —classical HTML for terminal window browsing) is due.**Thu., Feb. 7:****Read:**§§ 3.1 – 3.3

**Exercises:****Tue., Feb. 5:****Read:**§§ 2.5 – 2.6

**Exercises:**Online slides (Firefox or IE+MathPlayer or PDF) for the class are available.

**Thu., Jan. 31:****Read:**§§ 2.1 – 2.4

**Exercises:**Post assignment: online slides (Firefox or IE+MathPlayer or PDF) for the last exercise are available.

**Tue., Jan. 29:**- Acquire the textbook.
Read through chapter 1, and try some of
what is sketched there for yourself in
*Maple*.**About free**The following items were found through a web search, but none of them have been reviewed.*general purpose*computer algebra systems:*Axiom*-
*Axiom*has been in development since 1973 and was sold as a commercial product. It has been released as free software under the Modified BSD License. It is sponsored by CAISS, the Center for Algorithms and Interactive Scientific Software, at The City College of New York. *Maxima*-
*Maxima*is a descendant of*Macsyma*, the computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. It is free under the GNU General Public License subject to some export restrictions from the U.S. Department of Energy. A proprietary version of*Macsyma*is also available. *SAGE*-
*SAGE*is something relatively new that is not a computer algebra system but rather a free unifying framework for various computer algebra systems, free and non-free, such as*Maple*,*Mathematica*,*Axiom*,*Maxima*, and a number of specialist systems.*SAGE*can be operated, even across the network (though usually not without permission), in the window of a web browser.

**Thu., Jan. 24:****First meeting:**No assignment.

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