Goto: Prof. King's page at Univ. of Florida.    Or: JK Homepage.
Prof. King's site Modified: Tuesday, 02Aug2016     Printed: Tuesday, 27Jun2017
Page: http://squash.1gainesville.com/Include/thispage.shtml
JK focus Articles Fonts
JK Contradance calling Dances/Composers (contradance) Tunes/Bands (contradance)
L0 Contradance program L1 Contradance program L2 Contradance program L3 Contradance program L4 Contradance program L5 Contradance program Jonathan's dances
testing Misc Navigation Schedule Teaching StanZas

Michael Dyck's Contradance Index LORs Pamphlets

  PAST-COURSES
Complex Vars 2017g SeLo 2017g
NumT 2016s NT & Math Crypto 2016g
LinA 2015t DfyQ 2015t
DfyQ 2015g (NO WEBPAGE) SeLo 2015g
Crypto 2014g SeLo 2013g
DfyQ 2013t SeLo 2013g Melrose Nemo Parade, 2015 Melrose Moon Parade, 2016
Aut2008: MAS3114 3241 Computational.Linear.Alg MWF7 LIT203

Math

(Note: Our classroom is on the 2nd floor of Little Hall, East wing, North side.)
The following came from Earliest Known Uses of Some of the Words of Mathematics.
ALGEBRA comes from the title of a work written in Arabic about 825 by al-Khowarizmi, al-jabr w'al-muqabalah, in which al-jabr means "the reunion of broken parts." When this was translated from Arabic into Latin four centuries later, the title emerged as Ludus algebrae et almucgrabalaeque.

In 1140 Robert of Chester translated the Arabic title into Latin as Liber algebrae et almucabala.

In the 16th century it is found in English as algiebar and almachabel, and in various other forms but was finally shortened to algebra. The words mean restoration and opposition.

In Kholâsat al-Hisâb (Essence of Arithmetic), Behâ Eddîn (c. 1600) writes, The member which is affected by a minus sign will be increased and the same added to the other member, this being algebra; the homogeneous and equal terms will then be canceled, this being al-muqâbala.

The Moors took the word al-jabr into Spain, an algebrista being a restorer, one who resets broken bones. Thus in Don Quixote (II, chap. 15), mention is made of un algebrista who attended to the luckless Samson. At one time it was not unusual to see over the entrance to a barber shop the words Algebrista y Sangrador [bonesetter and bloodletter] (Smith vol. 2, pages 389-90).

The earliest known use of the word algebra in English in its mathematical sense is by Robert Recorde in The Pathwaie to Knowledge in 1551: Also the rule of false position, with dyvers examples not onely vulgar, but some appertayning to the rule of Algeber.

The phrase an algebra is found in 1849 Trigonometry and Double Algebra by Augustus de Morgan: Ordinary langauge has methods of instantaneously assigning meaning to contadictory phrases: and thus it has stronger analogies with an algebra (if there were such a thing) in which there are preorganized rules for explaining new contradictory symbols as they arise, than with one in which a single instance of them demands an immediate revision of the whole dictionary [University of Michigan Historical Math Collection]. …

Real Analysis is no more about reality than Complex Analysis is about complexity.
-P. Boyland, paraphrased
The following is from Wikipedia, the free encyclopedia

Cryptography (or cryptology; derived from Greek κρυπτός kryptós "hidden," and the verb γράφω gráfo "write") is the study of message secrecy. In modern times, it has become a branch of information theory, as the mathematical study of information...

... Steganography (i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, from Herodotus, concealed a message - a tattoo on a slave's shaved head - by regrown hair. More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information .

Ciphertexts produced by classical ciphers always reveal statistical information about the plaintext, which can often be used to break them. After the Arab discovery of frequency analysis (around the year 1000), nearly all such ciphers became more or less readily breakable by an informed attacker. ... Essentially all ciphers remained vulnerable to cryptanalysis using this technique until the invention of the polyalphabetic cipher by Leon Battista Alberti around the year 1467. Alberti's innovation was to use different ciphers (ie, substitution alphabets) for various parts of a message (often each successive plaintext letter). He also invented what was probably the first automatic cipher device, a wheel which implemented a partial realization of his invention. In the polyalphabetic Vigenère cipher, encryption uses a key word, which controls letter substitution depending on which letter of the key word is used.



The following is abridged from Wikipedia, the free encyclopedia

Diophantus of Alexandria - (Greek: Διόφαντος ὁ Ἀλεξανδρεύς , circa 200/214 – circa 284/298)  was a Greek mathematician of the Hellenistic era. Little is known of his life except that he lived in Alexandria, Egypt ...

He was known for his study of equations with variables which take on rational values and these Diophantine equations are named after him. Diophantus is sometimes known as the father of Algebra. He wrote a total of thirteen books on these equations. Diophantus also wrote a treatise on polygonal numbers.

In 1637, while reviewing his translated copy of Diophantus' Arithmetica (pub. ca.250) Pierre de Fermat wrote his famous Last Theorem in the page's margins. His copy with his margin-notes survives to this day.

Although little is known about his life, some biographical information can be computed from his epitaph (see links below). He lived in Alexandria and he died when he was 84 years old. Diophantus was probably a Hellenized Babylonian.

A 5th and 6th century math puzzle involving Diophantus' age: He was a boy for one-sixth of his life. After one-twelfth more, he acquired a beard. After another one-seventh, he married. In the fifth year after his marriage his son was born. The son lived half as many as his father. Diophantus died 4 years after his son. How old was Diophantus when he died?



The answer: 84 The answer is determined from two methods: 1. Finding the common multiple of 12, 6, and 7 (which is 84). 2. Taking 14 (the age up to which would be considered a boy; one-sixth of his life) multiplied by 6, which equals 84.

Tips on writing proofs

Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the ChecklistThe checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).


This branch of mathematics is the only one, I believe, in which good writers frequently get results entirely erroneous. ... It may be doubted if there is a single extensive treatise on probabilities in existence which does not contain solutions absolutely indefensible.
C. S. PEIRCE,
in Popular Science Monthly (1878).
I recoil with dismay and horror at this lamentable plague of functions which do not have derivatives.
-Charles Hermite


There's a delta for every epsilon,
It's a fact that you can always count upon.
There's a delta for every epsilon
        And now and again,
        There's also an N.

But one condition I must give:
The epsilon must be positive
A lonely life all the others live,
        In no theorem
        A delta for them.

How sad, how cruel, how tragic,
How pitiful, and other adjec-
Tives that I might mention.
The matter merits our attention.
If an epsilon is a hero,
Just because it is greater than zero,
It must be mighty discouragin'
To lie to the left of the origin.

This rank discrimination is not for us,
We must fight for an enlightened calculus,
Where epsilons all, both minus and plus,
        Have deltas
        To call their own.
  
Words and Music by Tom Lehrer,
American Mathematical Monthly, 81 (1974)
The following is from Wikipedia, the free encyclopedia

Linear Algebra – Linear algebra stems from the need to solve systems of linear equations. For small systems, ad hoc methods are sufficient. Larger systems require one to have more systematic methods. The modern day approach can be seen 2,000 years ago in a Chinese text, the Nine Chapters on the Mathematical Art (Traditional Chinese: 九章算術; Simplified Chinese: 九章算术; pinyin: Jiǔzhāng Suànshù).

Chinese mathematicians developed a system in which they organized linear equations in a rectangular pattern called Fāng Chéng (方程) in Chinese, involving horizontal and vertical counting rods. This rectangular representation of linear equations is the equivalent of today's matrix.

One of the key developments in linear algebra was the modern day method of solving linear systems known as Gauss-Jordan elimination, after German mathematician Carl Friedrich Gauss (1777-1855) and German engineer Wilhelm Jordan (1844-1899). Gauss called the method eliminatio, even though the Chinese were using an almost identical method nearly two millennia prior. This method stemmed really from Gauss's laziness in leaving off variable stems such as x1, x2, etc. in solving large n-tuples of linear equations while following the asteroid now known as Ceres. His method is explained in his book Theoria Motus Corporum Coelestium (1809).

The following is from Earliest Known Uses of Some of the Words of Mathematics
NUMBER THEORY. According to Diogenes Laertius, Xenocrates of Chalcedon (396 BC - 314 BC) wrote a book titled The theory of numbers.

A letter written by Blaise Pascal to Fermat dated July 29, 1654, includes the sentence, The Chevalier de Mèré said to me that he found a falsehood in the theory of numbers for the following reason.

The term appears in 1798 in the title Essai sur la théorie des nombres by Adrien-Marie Legendre (1752-1833).

In English, theory of numbers appears in 1811 in the title An elementary investigation of the theory of numbers by Peter Barlow.

Number theory appears in 1853 in Manual of Greek literature from the earliest authentic periods to the close of the Byzantine era by Charles Anthon: "The ethics of the Pythagoreans consisted more in ascetic practice and in maxims for the restraint of the passions, especially of anger, and the cultivation of the power of endurance, than in scientific theory. What of the latter they had was, as might be expected, intimately connected with their number-theory" [University of Michigan Digital Library].

Number theory appears in 1864 in A history of philosophy in epitome by Dr. Albert Schwegler, translated from the original German by Julius H. Seelye: "Not only the old Pythagoreans, who have spoken of him, delighted in the mysterious and esoteric, but even his new-Platonistic biographers, Porphyry and Jamblichus, have treated his life as a historico-philosophical romance. We have the same uncertainty in reference to his doctrines, i. e. in reference to his share in the number-theory. Aristotle, e. g. does not ascribe this to Pythagoras himself, but only to the Pythagoreans generally, i. e. to their school" [University of Michigan Digital Library]. ...

At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist Checklist (pdf, 3pages) to earn full credit.

Quantifiers and (“for all”  and  “there exists”) are like nitroglycerin, in that one little mis-step leads to the whole thing blowing up in your face.

There is no partial credit when it comes to Explosives and Quantifiers.

-JLF King

We are sorry, but the number you have dialed is imaginary. Please rotate your phone by 90 degrees and try again.
-David Grabiner

The four-year-old niece of a mathematician was playing a game in which she was the conductor on a train and her mother was a passenger. Wait a minute, said Nancy, we have to get some paper to make tickets. Oh, said her mother, who had probably had a long day, do we really need them? After all, it's only a pretend game with pretend tickets.

    Oh no, Mommy, you're wrong, replied Nancy; they're pretend tickets, but it's a  real  game.


(recounted by David Gale. This appeared
in The Intelligencer.)

(Announcement of a Special Topics course, under the course number MAT4930.)

I will be running a Special Topics NT course for Fall 2007, as long as it has at least 14 students.

This course does NOT require NT 1 (MAS4203). [For those who have already taken MAS4203, I have designed this course to be a good successor.] For students who have not already taken MAS4203, I ask that (during the summer) they read about 30 pages from Shoup's free online text [linked below].

From the undergraduate chairman:
This course will counted as a math-major elective and as one of the three 4000-level math courses required for the math minor, but ISIS will not know this; you'll have to ask the Undergraduate Coordinator to adjust your audit after the fall semester has begun.

If potentially interested in taking the course, please email me at
squashATuflDOTedu (Prof. JLF King)
and I will add you to the mailing list. Most of the information about the course will be distributed by email.

Our course is a 3 credit course.
I was just informed that one must register at the Math department for any of the Special Topics courses.
As you can see on my Schedule So much to do, so little Time... I will have my 2006 office-hours on 7th-period. I also have OH by appointment, but if you are able to keep one of M,W,F-7th free for office-hours, that would be convenient for you and me.

Welcome! Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the ChecklistThe checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).

In all of my courses, attendance is absolutely required (excepting illness and religious holidays). In the unfortunate event that you miss a class, you are responsible to get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.

General Info

A syllabus (text file) is available. On the first day of class I will hand-out a paper syllabus, which has the instructions on how to use the class archive. The archive is at a private URL, only for the use of the students in our class.

Whatever you do, Don't look at Past courses with notes, exams and links!

There  will be  was  a test of prerequisite knowledge on Wedn., 11Jan..

Friday., 13Jan., is the Last day of Add/Drop, so that students can self-evaluate if they should be in the course. The mini-test will count for 6%—8% of course grade.

The mini-test will select some topics from:

If you missed the prereq exam, you must make it up posthaste; Thursday midafternoon at the latest.

Here is a sample test (pdf) [Image: Updated] which is longer than the actual one will be. Note that this is an open brain closed text, no calculator exam.

There was a test of prerequisite knowledge (pdf) on Friday, 07Jan2011. Our mini-test will count for 7%—9% of course grade.

If you missed the prereq exam, you must make it up posthaste. Please email me immediately at squashATuflDOTedu (Prof. Jonathan King)

Tuesday, 11Jan2011, is the Last day of Add/Drop; students can self-evaluate if they should be here, or if they should transfer to Intro Number Theory, MAS4203 8430, MWF4 LIT219, Prof. Alladi.

The mini-test will examine beginning NT topics, Modular arithmetic, Euler-phi fnc, Chinese Remainder Theorem as well as basic facts on primes and a beginning-level NT proof or Induction proof.

It will also select topics from your Calc 1,2 knowledge (Differentiation rules, Integration, basic series), and High-school knowledge (formula for a line between two points, the Quadratic Formula, intersecting a line with a parabola, etc.) and the Math-Greek alphabet (pdf), which we will use in class frequently.

Here is a sample test (pdf) which is longer than the actual one will be. This is an open brain, closed text, no calculator exam.

There will be a test of prerequisite knowledge Monday, 27Aug2007. Observe that Wedn., 29Aug, is our Last class-day of Add/Drop, so that students can self-evaluate if they should be in the course. The mini-test will count for 6%—9% of course grade.

The mini-test will select some topics from your Calc 1-3 knowledge (Integration by parts, Intermediate-Value Thm and Mean-VT. Multi-variate chain rule, Taylor series, Multiple integrals, etc.), and High-school knowledge (formula for a line between two points, the Quadratic Formula, intersecting a line with a parabola, etc.) and the Math-Greek alphabet (pdf), which we will use in class frequently.


The various Number Theory czars who help out.

Projector Phone-list Chalk Blackboard H-Probs Time
? ? Charlye Marshall Jimmy-C & Dream Cameron

Our textbook is Math (Third Edition Update).
Author: David Lay Year: 2006
ISBN: 0-321-28713-4 Publisher: Addison-Wesley
Here are links to this book at The Publisher's site and at Amazon.com.

Optional end-of-semester project

There will be not be a final exam .   Rather, there will be an optional end-of-semester project, to be done individually. The project will be due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , no later than noon, Friday, 12Dec2008.

The final project must be carefully typed. I recommend learning the free mathematics-typesetting language LaTeX. (It is the archive language of the American Mathematical Society.) It can be learned in a week. It is very good for typesetting homework.


At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist Checklist (pdf, 3pages) to earn full credit.

Prof. Jonathan King
Office: 402 Little Hall (NE corner)
OfficeTel: 392-0281 x270
MathDept: LIT366
MathDeptTel: 392-0281 x221,223
Atrium:  LIT339 (Colloquia are held here)
Eddress: squashATuflDOTedu
    Teaching Page: http://squash.1gainesville.com/teaching.html
    Footnotes: http://squash.1gainesville.com/info.footnote.html

1 JK Course Template

fdkd dkdkk abced

22 JK Course Template

fdkd dkdkk abced

22 icon Course Template

fdkd dkdkk abced

333 JK Course Template

fdkd dkdkk abced

4444 JK Course Template

fdkd dkdkk abced
55555 JK Course Template
fdkd dkdkk abced
55555 ICON Course Template
fdkd dkdkk abced
666666 JK Course Template
fdkd dkdkk

JK Home page Goto jk HomePage

____End: Math Page