Carl Friedrich Gauss

· German Mathematician

· Born April 30, 1777; Died February 23, 1855

· “Prince of Mathematicians”

· Contributed to numerous fields including: number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, and astronomy

· Contribution in the field of: NUMBER THEORY

· 1798 (Published 1801)-Disquisitiones Arithemeticae was fundamental in consolidating number theory as a discipline and has made an impact until current day.

· This book introduced the first account of modular arithmetic, gives a thorough account of the solutions of quadratic polynomials in two variables in integers, and ends with the theory of factorization. This book set the agenda for number theory in the 19th century.

· Influence can be seen through work with Complex numbers

· He gave the first clear explanation of complex numbers and of the investigation of functions of complex variables in the early 19th Century.

· He was responsible for popularizing the practice of illustrating how complex numbers are related to real numbers via graphs.

http://www.storyofmathematics.com/19th_gauss.html

Marie-Sophie Germain

· French Mathematician

· Born April 1, 1776—died June 27, 1831

· Contributed to numerous fields including: elasticity and number theory

· Contributions to: NUMBER THEORY

· Went against her family’s wishes and social prejudice to become mathematician

· Corresponded in depth with Gauss and Legendre outlining her strategy to solving Fermat’s Last Theorem

· She proved the special case in which x, y, z, and n are all relatively prime (have no common divisor except for 1) and n is a prime smaller than 100

· Proved that if x, y, and z are integers and if x^5+y^5=z^5 then either x, y, or z must be divisible by 5

· Work was a major step towards proving Fermat’s Last theorem.

· Published in 1825 in the second edition of Legendre’s Théorie des nombres

http://www.britannica.com/EBchecked/topic/230626/Sophie-Germain

Pierre de Fermat

· French lawyer and amateur mathematician

· Born August 1601 – Died January 12, 1665

· Contributions in the fields of analytic geometry, probability, and number theory

· Contribution in: NUMBER THEORY

· Fermat posed the questions and identified the issues that have shaped number theory

· 1640-Fermat’s Little Theorem- if p is prime and a is any whole number, then p divides evenly into ap − a. Thus, if p = 7 and a = 12, the far-from-obvious conclusion is that 7 is a divisor of 127 − 12 = 35,831,796

· He investigated the two types of odd primes: those that are one more than a multiple of 4 and those that are one less. These are designated as the 4k + 1 primes and the 4k − 1 primes

· 1638- asserted that every whole number can be expressed as the sum of four or fewer squares

· 1637- Fermat’s Last Theorem- the statement that there are no natural numbers (1, 2, 3, …) x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2.

http://www.britannica.com/EBchecked/topic/422325/number-theory/233901/Pierre-de-Fermat

Diophantus of Alexandria

· Grecian mathematician

· Born 200- Died 284

· “Father of Algebra”

· Contributions to Algebra and number theory

· Contribution in: ALGEBRA

· Arithmetica-work on the solution of algebraic equations and on the theory of numbers

· This book is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations

· This way of solving problems is known as “Diophantine analysis”

· Work in quadratic equations:

· Diophantus looked at three types of quadratic equations ax2 + bx = c, ax2 = bx + c and ax2 + c = bx. The reason why there were three cases to Diophantus, while today we have only one case, is that he did not have any notion for zero and he avoided negative coefficients by considering the given numbers a, b, c to all be positive in each of the three cases above.

· Introduced the use of symbols for unidentified quantities in his equations

· Used fractions as numbers and his equations were considered the epitome of algebra

http://www.famous-mathematicians.com/diophantus/

Julia Bowman Robinson

· American Mathematician

· Born December 1919-died July 1985

· Contribution to: ALGEBRA

· Graduated from San Diego State University

· During WWII, she worked for Jerzy Neyman in the Berkeley Statistical Laboratory on secret military projects.

· Her Ph.D. dissertation proved the algorithmic unsolvability of the theory of the rational number field

· Worked for 20 years on the Tenth Problem of David Hilbert’s problem to find an effective method for determining if a given Diophantine equation is solvable in integers

· 1961-presented the Davis-Putnam-Robinson paper which served as the foundation to proving that there is NOT a general method for determining solvability.

· First woman mathematician elected to the National Academy of Sciences in 1975

· Elected the first woman president of the American Mathematical Society in 1982

· Awarded the MacArthur Foundation Prize Fellowship of $60,000 for 5 years

Omar Khayyam

· Persian mathematician and philosopher

· Born 1048- Died

· Contribution to: ALGEBRA

· 1070-Treatise on Demonstration of Problems of Algebra

· Discovered a general method of extracting roots of arbitrary high degree

· Laid the foundation for Pascal’s Triangle

· first complete treatment of the solution of cubic equations

· Omar did this by means of conic sections, but he declared his hope that his successors would succeed where he had failed in finding an algebraic formula for the roots.

http://www.famous-mathematicians.com/omar-khayyam/#citethis

http://www.britannica.com/EBchecked/topic/369194/mathematics/65994/Omar-Khayyam

Rene Descartes

· French mathematician and philosopher

· Born 1596- Died 1650

· “Father of Analytical Geometry”

· Contribution to: GEOMETRY

· Main achievement was creating a bridge between algebra and geometry

· Father of Analytical Geometry:

· Great advance made by Descartes was that he saw that a point in a plane could be completely determined if its distances, say x and y, from two fixed lines drawn at right angles in the plane were given, with the convention familiar to us as to the interpretation of positive and negative values; and that though an equation f(x,y) = 0 was indeterminate and could be satisfied by an infinite number of values of x and y, yet these values of x and y determined the co-ordinates of a number of points which form a curve, of which the equation f(x,y) = 0 expresses some geometrical property, that is, a property true of the curve at every point on it

· Created the Cartesian Coordinate System

· Explained the algebraic equations through geometric shapes

· Invented the convention of representing unknowns in equations with x, y, z

http://www.maths.tcd.ie/pub/HistMath/People/Descartes/RouseBall/RB_Descartes.html

http://www.famous-mathematicians.com/rene-descartes/

Pythagoras

· Ionian Greek philosopher

· Born 570 BC- Died 495 BC

· Contribution to: GEOMETRY

· Pythagorean Theorem

· states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides—that is, .

http://en.wikipedia.org/wiki/Pythagoras

http://www.cis.yale.edu/ynhti/curriculum/units/1984/2/84.02.05.x.html

Euclid

· Greek mathematician

· Born 325 BC-Died 265 BC

· Contribution in: GEOMETRY

· Elements-Compilation of the previous works of other men, mathematicians, and philosophers

· Euclid’s Postulates:

· five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions

http://www.britannica.com/EBchecked/topic/194880/Euclid

Augustin-Louis Cauchy

· French Mathematician

· Born August 1789- Died May 1857

· One of the greatest modern mathematicians

· Contribution to: CALCULUS

· Cours d’analyse de l’École Royale Polytechnique (1821; “Courses on Analysis from the École Royale Polytechnique”)

· Introduced inequalities to Calculus and arguments

· Résumé des leçons sur le calcul infinitésimal (1823; “Résumé of Lessons on Infinitesimal Calculus”)

· Leçons sur les applications du calcul infinitésimal à la géométrie (1826–28; “Lessons on the Applications of Infinitesimal Calculus to Geometry”).

· Clarified the principles of Calculus by developing it with the use of limits and continuity

http://www.britannica.com/EBchecked/topic/100302/Augustin-Louis-Baron-Cauchy

Grace Chisholm Young

· English Mathematician

· Born March 1868-died 1944

· Contribution to: CALCULUS

· Graduated from Cambridge

· 1895 wrote thesis “Algebraisch-gruppentheoretische Untersuchungen zur spharischen Trigonometrie” or “Algebraic Groups of Spherical Trigonometry”

· Researched areas such as the topology of the real line and plane, measure theory and integration, Fourier series, and the foundations of differential calculus

· Grache wrote 18 mathematical articles

· Won the 1915 Gamble Prize at Cambridge for an essay on the foundations of calculus.

· Denjoy-Young-Saks theorem

· If f is a real valued function defined on an interval, then outside a set of measure 0 the Dini derivatives of f satisfy one of the following four conditions at each point:

· f has a finite derivative

· D+f = D–f is finite, D–f = ∞, D+f = –∞.

· D–f = D+f is finite, D+f = ∞, D–f = –∞.

· D–f = D+f = ∞, D–f = D+f = –∞.

Gottfried Wilhelm Leibniz

· German mathematician and philosopher

· Born 1646- Died 1716

· Contribution to: CALCULUS

· Discovery of infinitesimal calculus: comprises differential and integral calculus

· 1675-employed integral calculus for the first time to find the area under the graph of a function y = ƒ(x).

· Introduced the integral sign

· Leibniz’s law

· The product rule of differential calculus: Simply, if u and v are two differentiable functions of x, then the differential of uv is given by: this can also be written, using 'prime notation' as :

· Leibniz’s integral rule:

· if we have an integral of the form then for x in (x0, x1) the derivative of this integral is thus expressible provided that f and its partial derivative fx are both continuous over a region in the form [x0, x1] × [y0, y1].

http://plato.stanford.edu/entries/leibniz/; http://en.wikipedia.org/wiki/Leibniz_integral_rule

Sir Isaac Newton

· English physicist and mathematician

· Born December 1642- Died March 1727

· “Father of Calculus”

· Contribution to: CALCULUS

· Principia-book developing infinitesimal calculus

· applied calculus for several purposes: finding areas, tangents, the lengths of curves and the maxima and minima of functions

· Fundamental Theorem of Calculus:

· the first fundamental theorem of calculus, is that an indefinite integration can be reversed by a differentiation

· the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely many antiderivatives

http://www.fabpedigree.com/james/mathmen.htm; http://en.wikipedia.org/wiki/Isaac_Newton

Georg Cantor

· German mathematician

· Born March 1845- Died 1918

· Contribution to: DISCRETE MATHEMATICS

· Inventor of Set Theory

· showed that, just as there were different finite sets, there could be infinite sets of different sizes, some of which are countable and some of which are uncountable

· 1880-1890 defined well-ordered sets and power sets and introducing the concepts of ordinality and cardinality and the arithmetic of infinite sets

· One-one Correspondence

· 1878- defined 1-to-1 correspondence, and introduced the notion of "power"or "equivalence" of sets: two sets are equivalent (have the same power) if there exists a 1-to-1 correspondence between them

http://en.wikipedia.org/wiki/Georg_Cantor; http://www.storyofmathematics.com/19th_cantor.html

Fan Chung

· Taiwanese Mathematician

· Born October 1949-

· Contribution to: DISCRETE MATHEMATICS

· Worked mainly in the areas of spectral graph theory, extremal graph theory and random graphs

· Erdos-Renyi model for graphs with general degree distribution

·

· Published more than 200 research papers and three books

· Erdos on Graphs: His Legacy of Unsolved Problems

· Spectral Graph Theory

· Complex Graphs and Networks

· 1974-became a member of Technical Staff working for the Mathematical Foundations of Computing Department at Bell Laboratories

· Created a solid base in the Spectral graph theory to the future graph theorists

· Combines algebra and graph perfectly

· Spectral graph theory studies how the spectrum of the Laplacian of a graph is related to its combinatorial properties.

· 1997 American Mathematical Society published Fan Chang’s book Spectral graph theory

Leonhard Euler

· Swiss mathematician

· Born April 1707- Died September 1783

· Contribution to: DISCRETE MATHEMATICS

· Graph Theory:

· Eulerian Trail: a trail in a graph which visits every edge exactly once. Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail which starts and ends on the same vertex

· Seven Bridges of Konigsberg:

· Famous problem on graph theory that Euler solved

· Euler’s Formula:

· Applies to all planar graphs

· Created the formula relating the number of edges, vertices, and faces

· Faces +vertices=edges+1

http://en.wikipedia.org/wiki/Graph_theory

http://www.jcu.edu/math/Vignettes/bridges.htm

Florence Nightingale

· British social reformer and statistician

· Born May 1820- Died August 1910

· Contribution to: STATISTICS

· “True pioneer in the graphical representation of statistics”

· Nightingale rose diagram

· Developed through her work in the Crimean War

· Created a pie chart called the polar area diagram

·

· Revolutionized the idea that social phenomena could be objectively measured and subjected to mathematical analysis.

http://en.wikipedia.org/wiki/Florence_Nightingale

http://malini-math.blogspot.com/2009/11/florence-nightingales-contribution-to.html

Daniel Bernoulli

· Swiss physician and mathematician

· Born 1700- Died March 1782

· Contribution to: STATISTICS

· 1738- Exposition on a New Theory on the Measurement of Risk

· St. Petersburg paradox-a paradox related to probability and decision theory in economics. It is based on a particular (theoretical) lottery game that leads to a random variable with infinite expected but nevertheless seems to be worth only a very small amount to the participants

· Theory on Risk aversion, Risk premium, and utility

· 1766 analysis of smallpox morbidity and mortality

· earliest attempts to analyze a statistical problem involving censored data

· modeled spread of smallpox

http://en.wikipedia.org/wiki/St._Petersburg_paradox

http://en.wikipedia.org/wiki/Daniel_Bernoulli;

http://statprob.com/encyclopedia/DanielBERNOULLI.html

Pierre- Simon Laplace

· French mathematician

· Born March 1749- Died March 1827

· Contribution to: STATISTICS and Probablity

· 1744-“Memoir sur la probabilite des causes par les evenements”

· 1747-second paper which discussed statistical theories, celestial mechanics, and the stability of the solar system

· 1779-Probability generating function:

· function treats the successive values of any other function as a coefficient when used to expand another function with a different variable

· Probability Laws:

· Probability can best be described as the ratio of favored events to possible events. This basic fact inspired the understanding of several more facts about probability and led Laplace to develop six very important laws or rules about the field

http://arithmetic.com/math/famous-mathematicians/pierre-simon-laplace.php

Archimedes

· Greek mathematician and philosopher

· Born 290 BC-Died 212 BC

· Contribution: MEASUREMENT SYSTEMS

· Measurement of a Circle:

· Used proof by contradiction

· Contained 3 propositions:

· The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle

· The area of a circle is to the square on its diameter as 11 to 14

· The ratio of the circumference of any circle to its diameter is greater than but less than

http://en.wikipedia.org/wiki/Archimedes

History of African Mathematics

· Middle Paleolithic 35,000 BC -30,000 BC

· 30,000 BC

· Lebombo bone

· a South African created the first counting stick

· 29 notches were cut into the stick

· Some hypothesize the tallies were counting days from one full moon to the next.

· Oldest mathematical object known

· Late Paleolithic 30,000 BC-7,000 BC

· 25,000 BC

· An Ishangan in East Africa created another tally stick.

· Second oldest mathematical object in Africa

· Had groups of marks.

· Originally said to be the oldest table of prime numbers but was later concluded to be a six month lunar calendar

· Neolithic Age 7,000-4,800 BC

· 7,000 BC-Egyptians and people from Sudan began using clay tokens to count

· Predynastic Period 4800-3050 BC

· Invention of 365 day calendar in 4200 BC

· By 3100 BC- various agricultural communities along the banks of the Nile were united by a Nubian, Menes, who founded a dynasty of 32 Pharaohs and lasted 3000 years

· Exhibited numbers to the millions

· 3,050 BC-2705 BC

· Archaic Period

· Egyptians began using hieroglyphics to write down large numbers

· Introduction of geometry to build pyramids

· Great pyramid of Giza built

· The Egyptian symbol for zero was introduced and used in the development of the pyramids

· 2705-2213 BC

· Old Kingdom

· Information is scarce, however:

· inscriptions on a wall near a mastaba in Meidum which gives guidelines for the slope of the mastaba

· The lines in the diagram are spaced at a distance of one cubit and show the use of that unit of measurement

· an efficient and extensive administration was developed for taking taxes, census, and maintaining a large army using counting glyphs

· Counting glyphs were hieroglyphic symbols used in combination to add and subtract

· 2213-2000 BC

· First Intermediate Period

· By 2000 BC the hieratic glyphs were in use to relay mathematical concepts and functions

· Not much is known from this time. It was considered the “dark period” because power was split between two competing bases one in Lower and one in Upper Egypt. The temples were pillaged and burned and most evidence of this time was destroyed.

· 2000-1650 BC

· Middle Kingdom

· The same zero symbol was used to express zero remainders in a monthly account sheet

· Moscow Papyrus contains 25 mathematical problems

· Problems written in hieroglyphics

· Approximately 18 feet long and varying between 1½ and 3 inches wide, its format was divided into 25 problems

· Covers ship parts problems, finding unknown quantities, division, worker output, and geometry problems

· 1650-1550 BC

· 2nd Intermediate Period

· Egyptian Mathematical Leather Roll

· 10 × 17 in leather roll

· an aid for computing Egyptian fractions. It contains 26 sums of unit fractions which equal another unit fraction.

· 1650 Ahmes/ Rhind Papyrus

· Written in the hieratic script, this Egyptian manuscript is 33 cm tall and consists of multiple parts which in total make it over 5m long.

· contains 85 mathematical problems

· contains a list of Egyptian fractions used for 2/n where n is an odd n umber from 3 to 101

· covers volumes, areas, pyramids, and multiplication and division of fractions

· 1570-1070 BC

· New Kingdom

· Papyrus Anastasi I

· ancient Egyptian papyrus containing a satirical text used for the training of scribes

· gives examples of what a scribe was supposed to be able to do: calculating the number of rations which have to be doled out to a certain number of soldiers digging a lake or the quantity of bricks needed to erect a ramp of given dimensions, assessing the number of men needed to move an obelisk or erect a statue, and organizing the supply of provisions for an army

· Papyrus Wilbour

· Records how to measure land as and serves as a record of land measurement

· Records volumes of dirt removed or moved during building tombs

· 1070BC-685 BC

· Late Period

· Gebet'a or "Mancala" Game

· game forces players to strategically capture a greater number of stones than one's opponent

· in antiquity, the holes were more likely to be carved into stone, clay or mud

·

· 685 BC- 525 BC

· Saite Period

· Not much is known from this period as many battles took place during this time

· Fall of Ashdod refers to the successful Egyptian assault on the city of Ashdod in Palestine in c. 635 BC- lasted 29 years

· Battle of Megiddo is recorded as having taken place in 609 BC with Necho II of Egypt leading his army to Carchemish to fight with his allies the Assyrians against the Babylonians

· In 605 Babylonians defeated Egyptians

· Battle with the Persians began

· Battle of Pelusium- the first major battle between the Achaemenid Empire and Egypt; battle transferred the throne of the Pharaohs to Cambyses II of Persia, king of the Persians

· 525BC- 332BC

· Phoenicians colonized North Africa

· Introduced the West Asian systems of counting and writing numbers

· 332 BC-411 AD

· Romans colonized and opened schools in North Africa

· Taught Greek geometrical proofs

· Hypatia an Alexandrian mathematician

· First well documented woman in mathematics

· worked on proving things about the geometry of cones and what happened when a cone was intersected by a plane

· A commentary on the 13-volume Arithmetica by Diophantus.

· A commentary on the Conics of Apollonius.

· Edited the existing version of Ptolemy's Almagest.

· Edited her father's commentary on Euclid's Elements

· She wrote a text "The Astronomical Canon"

· 150 AD Ptolmey of Alexandria

· Planetary Hypotheses- went beyond the mathematical model of the Almagest to present a physical realization of the universe as a set of nested spheres

· correctly estimated pi to be 3+10/71

· 411 AD-500 AD

· Not much is known about this time as major battle and changes were taking place throughout Africa.

· The decline in trade weakened Roman control. Independent kingdoms emerged in mountainous and desert areas, towns were overrun, and Berbers, who had previously been pushed to the edges of the Roman Empire, returned

· War between the Romans and Muslims caused much destruction

· 500-1248 AD

· Islamic Golden Age

· Abu Kamil

· Egyptian Muslim mathematician

· first mathematician to systematically use and accept irrational numbers as solutions and coefficients to equations

· first Islamic mathematician to work easily with algebraic equations with powers higher than x^2 (up to x^8),and solved sets of non-linear simultaneous equations with three unknown variables

· Arab invaders took over most of Northern and Eastern Africa

· brought with them their religion, Islam, and new ways of counting

· Explained how to use zero as a place-holder. Zero made it much easier to do math.

· Timbuktu Mathematical Manuscripts

· Many of the scripts were mathematical and astronomical in nature.

· As many as 700,000 scripts have been rediscovered and attest to the continuous knowledge of advanced mathematics and science in Africa well before European colonization

·

· 1000 AD

· West Africans were using a number system which was partly in base ten and partly in base twenty.

· Unlike the Indian/Arab math that only used addition, the West African counting also used subtraction

· West Africans were also using cowrie shells for counting

· 1100-1200

· Al-Qurash

· worked on algebra

· wrote a commentary on the work of the Egyptian mathematician Abu Kamil

· invented a new method for reducing fractions

· Al-Hassar

· a Muslim mathematician from Morocco

· author of two books Kitab al-bayan wat-tadhkar (Book of Demonstration and Memorization)

· manual of calculation and Kitab al-kamil fi sinaat al-adad (Complete Book on the Art of Numbers

· the first book is lost and only a portion of the second book remains

· developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar.

· Ibn al-Yasamin

· Moroccan mathematician

· Talqih al-afkar bi rushum huruf al-ghubar (Fertilization of Thoughts with the Help of Dust Letters

· book of two hundred folios about (among other things) the science of calculation and geometry

· wrote three poems (urzaja), one on algebra, one on irrational quadratic numbers and one on the method of false position.

· 1200-1400

· Ibn al-Banna

· Morrocan mathematician

· wrote between 51 to 74 treatises, encompassing such varied topics as Algebra, Astronomy, Linguistics, Rhetoric, and Logic.

· Talkhīṣ ʿamal al-ḥisāb (Summary of arithmetical operations

· topics such as fractions, sums of squares and cubes

· Tanbīh al-Albāb

· calculations regarding the drop in irrigation canal levels,

· arithmetical explanation of the Muslim laws of inheritance

· determination of the hour of the Asr prayer,

· explanation of frauds linked to instruments of measurement,

· enumeration of delayed prayers which have to be said in a precise order,and

· calculation of legal tax in the case of a delayed payment

· 1400-1700

· Not much is known as the slave trade grows exponentially and millions of Africans are captured, kidnapped and shipped elsewhere as well as massive and constant war across the continent.

· In the North there was war with the muslims, Christian missionaries, the Ottoman Empire, and England

· Rwanda had the Tutsi and Hutu

· West Africa and Central Africa had the Portuguese and different African empires fighting

· Southern African involved fighting between the Dutch, British, and French

· Portugese invade Western Africa

· Exploration begins in 1415

· 175,000 slaves taken and the slave trade is only at its beginning

· Found thriving large cities with developed governments and agriculture systems

· Ibn al-Majdi

· an Egyptian mathematician and astronomer

· "Book of Substance", a voluminous commentary on Ibn al-Banna''s Summary of the Operations of Calculations

· Ibn Gahzi al-Miknasi

· a Moroccan scholar in the field of history, Islamic law, Arabic philology and mathematics

· Bughyat al-tulab fi sharh munyat al-hussab ("The desire of students for an explanation of the calculator's craving")

· Included sections of arithmetic and algebraic methods

· 1700-1900

· Europeans joined the slave trade and by 1898 conquered most of Africa

· Portuguese owned the western part of Africa

· Europeans pillaged and took the necessary materials needed for their country killing many Africans

· Francis Guthrie

· South African mathematician

· 1852-Posed Four Colour problem

· given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions

· Remained unsolved for more than a century

· 1900-Present

· Decolonization began

· Bitter wars of independence in many African countries began

· Africans began to gain a voice and freedom again

· African mathematicians began to flourish

· Caleb Gattegno

· Egyptian scholar

· known for his innovative approaches to teaching and learning mathematics

· George Saitoti

· Kenyan mathematician

· Head of the Mathematics Department at the University of Nairobi, pioneered the founding of the African Mathematical Union and served as its Vice-President from 1976–1979

· Institutionalized Mathematics as a discipline in Africa

· Chike Obi

· Nigerian mathematician

· First African to hold a doctorate in Math

· Established Nanna Institute of Scientific Studies

· 1997 claimed to have an elementary proof of Fermat’s Last Theorem

· However this was later proved to be false

· Chris Brink

· South African mathematician

· Pioneered the study of Boolean modules over relation algebras

· provide a modern formalization of Peirce's logic of relatives in terms of universal algebra.

· Lionel Cooper

· South African mathematician

· worked in operator theory, transform theory, thermodynamics, functional analysis and differential equations.

· Operator Theory

· worked in the area of linear operators on real or complex Hilbert spaces

· studied the unbounded operators that arose from quantum theory, extending basic work of Frigyes Riesz and John von Neumann.

· Transform Theory

· worked on the representation and uniqueness of integral transforms, on approximation, and on linear transformations that satisfy functional relations arising from representations of linear groups

· Stanley Skewes

· South African mathematician

· Skewes number

· any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which where π is the prime-counting function and li is the logarithmic integral function

http://www.historyforkids.org/learn/africa/science/numbers.htm

http://www.taneter.org/math.html

http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egypt.html#egyptian origins

http://en.wikipedia.org/wiki/Egyptian_mathematics

http://en.wikipedia.org/wiki/Category:African_mathematicians

http://en.wikipedia.org/wiki/History_of_Africa

Incorporating History into:

GEOMETRY

Throughout the school year students will be keeping a math journal. Normally it is setup with the left page covering the topic, where it can be seen in real life, definitions, theorems, and key notes. The right page is dedicated to vocabulary. The student finds or draws pictures of new vocabulary and where they are seen in real life. They then create definitions in their own words. An example is shown below:

However, in order to incorporate the history behind the math, I have altered the pages to also include a section dedicated to the mathematicians as well. Each day that we begin a new topic the following will take place:

-I will introduce the lesson/mathematician through a Bell Ringer at the start of class. This can be a thought provoking question, video clip, Think Pair Share activity and other interactive strategies.

-After sparking interest about the topic, I will cover a brief history of the mathematician and his discovery. I will pass out a small half page of history along with that discussion.

-The lesson for the day will also link back to the history of the topic.

-I have included a few examples of how I plan to incorporate the history at various times, as well as student interaction and accommodations for special education students.

Pythagoras and the Pythagorean Theorem

I will begin the class with a bell ringer to assess the students’ prior knowledge. The bell ringer will consist of a word problem where Bob is trying to find the quickest route from point A to point C, but the only route he knows is to travel 3 feet east and 4 feet north. For students who are visually impaired or are ELL’s I will provide a visual representation to help them understand what the question is asking. After a few minutes, the students will pair with the person next to them to talk about what they did. The pairs will then share their results. This method will also benefit special education students and ELLs because peer interaction is very important for making meaning to a topic. It also gets all of the students involved in discussion.

After the bell ringer I will introduce Pythagoras and the Pythagorean Theorem. We will discuss briefly his life as a mathematician and philosopher and his greatest contribution, that a^2 +b^2= c^2. The students will add these notes to their journals. They will have 10 minutes to add the new vocabulary like triangle and hypotenuse to their journals as well.

I will then spend 15-20 minutes explaining the Pythagorean Theorem and working through examples with the students. Following my explanation, I will pass out to each student a set of 10 different triangle shaped cut outs, a ruler, and a key where different numbers equal different letters. At the bottom of the key there will be 10 numbers in a row. The students will use their rulers to measure the two sides (a and b) and use the Pythagorean Theorem to find c. The answer for c should match a letter listed in the key. They will then write that letter at the bottom of the page. They will repeat this for all 10 triangles and at the end if they did the activity correctly, the students should spell PYTHAGORAS. This activity is great for special education students and all students because it is interactive with both manipulatives and visuals. I will be walking around for extra assistance and guidance for any students who are struggling, and students are also allowed to work in pairs for added assistance and scaffolding.

(The key will resemble this type of problem, but the question will relate to Pythagoras)

Pi Day

On March 14th (Pi Day) we will discuss pi and the development of its approximation. Today’s lesson is more of a mini review/ history lesson and celebration of all of our work. The morning will begin with our daily bell ringer; however, it will simply be a picture of pi. I will ask the class to reflect on the visual and talk with a partner about what it is, represents, and the value of pi. We will discuss these questions then as a class and have a competition of who can name the most places of pi. This bell ringer is both interactive between classmates, but the think pair share method also relieves pressure from students who may not know much or anything about the topic.

Following the bell ringer I will give a short recap of the approximation of pi. I will show the actual value of pi, as well as talk about some of the many mathematicians who have played a role in attaining this approximation. Some of these mathematicians include Ahmes and the Rhind Papyrus, Archimedes, Aryabhata, Madhava, Chudnovsky brothers, and Fabrice Bellard.

I will then bring out a selection of 5-6 pies of varying flavor, which we will use to practice reviewing the unit circle. I will write different problems involving pi, the unit circle, or the history of pi on the board and students will take turns answering. In order to get a slice of pie the students must answer the question correctly and be able to give a short explanation of how they found that answer. This jeopardy type game is interactive and engaging. It requires students to tap into previous lessons and material and also gets them thinking about how they came to an answer. I believe being able to articulate not only how to do something but why you are doing it is extremely important.

After everyone has gotten a slice, students will be able to share different work that they have completed throughout the year and are proud of with the class. I will also use this time to ask the students what they have liked about the class, what they would like to see change, and how I could better my teaching. I feel self-reflection is extremely important to be able to grow as a person and educator.