and the spelling should be correct. It should include information about the subject’s early life, family, accomplishments, interesting **facts** and, if appropriate, death. At least three sources are required and will be properly cited on a separate page. / and went on to do important work in mathematics, especially her work on Fermats Last Theorem. **CARL** **FRIEDRICH** **GAUSS** (APRIL 30, 1777 – FEBRUARY 23, 1855) Child prodigy **Gauss**, the ‘Prince of Mathematics, made his first major discovery as a teenager. He wrote a /

of data points with a quadratic function. The least-squares method is usually credited to **Carl** **Friedrich** **Gauss** (1795), but it was first published by Adrien-Marie Legendre. **Carl** **Friedrich** GaussAdrien-Marie Legendre Population growth model A population model is a type of mathematical model / a function at a chosen input value describes the best linear approximation of the function near that input value. In **fact**, the derivative at a point of a function of a single variable is the slope of the tangent line to /

using a law called **Gauss**’ law, developed by German mathematician and physicist **Carl** **Friedrich** **Gauss** (1777–1855). → → Instead of considering dE in a given charge distribution, **Gauss**’ law considers a hypothetical (imaginary) closed surface enclosing the charge distribution. **Gauss**’ law relates the /of electric field inside the surface as in this case, the total flux through this surface is in **fact** equal to zero 8/13 Erwin SitompulUniversity Physics: Wave and Electricity Checkpoint The figure below shows a /

. 1 + 2 < 180 . Euclid’s Postulates for Geometry Using only these five postulates, Euclid was able to prove all of the **facts** about geometry that were known at the time. For example, Theorem: The interior angles of every triangle add up to exactly 180 . 1 +/upon the same amazing insight… Janos Bolyai, in Hungary (18 years old) Nikolai Lobachevsky, in Russia (38 years old) **Carl** **Friedrich** **Gauss**, in Germany (58 years old) A Bold New Idea Maybe there is a simple explanation for why nobody had succeeded in/

Govindaswami discovered Newton **Gauss** Interpolation formula about 1800 years before Newton. Vateswaracharya discovered Newton **Gauss** Backward Interpolation formula about 1000/drawn as if by some hidden urge.” - **Friedrich** Mejer (English statesman) “If there is one /development, for it believes in self- liberation. ” - **Carl** G. Jung “The surgery of the ancient Indian physicians /at all promoting greatness of Hinduism. But just explaining the **facts** validated by various respected scholars. That’s why references /

zeta function have real part one-half. Trivial and Nontrivial Yes, we have spotted some zeros of the zeta function. In **fact** ζ is zero for every negative even whole number argument: –2, –4, –6, –8, –10, –12, / among mathematicians in Murray’s Human Accomplishment. Introverted, poor, ill, pious (Lutheran). Studied under **Gauss** at Göttingen. Brilliant imaginative mathematician. **Carl** **Friedrich** **Gauss** German, 1777-1855 Ranked 4th among mathematicians in Murray’s Human Accomplishment. Supervised Riemann’s doctoral /

Clerk Maxwell (1831 – 1879 ) Unified Electricity, Magnetism and Light (Electromagnetic Theory of Light) Johann **Carl** **Friedrich** **Gauss** (1777-1855) German mathematician and physical scientist contributed significantly to many fields including number theory, algebra, statistics, analysis, differential geometry/ If you conclude that the earth’s magnetic pole under Santa Claus’s reputed home is in **fact** a South magnetic pole, you will be correct. Electromagnetism Originally electricity and magnetism were thought of as/

is the Queen of the Sciences. **Carl** **Friedrich** **Gauss** (1777 - 1855) once said: mathematics Why did **Gauss** compare to the Queen? Because, both have two important attributes in common: Beauty and Power In **fact**, the of Mathematics are the two important/like ALGEBRA and TRIGONOMETRY The Power and Beauty of Mathematics Today, has increased manifold scientific and technological developments In **fact**, the astonishing of the present day world are mainly due to the advancement in the mathematical knowledge Influence of /

of electricity Lightning is electrical Use of electrical ground Andre Marie Ampere Ampere’s Law Pioneers of the Field Johann **Carl** **Friedrich** **Gauss** **Gauss**’s Law Pioneers of the Field Michael Faraday Faraday’s Law Pioneers of the Field George Gabriel Stokes Stokes’s /radio communication over a distance of 2000 miles in December 1901. Marconi was celebrated worldwide for this achievement, but the **fact** that the receiver was invented by Bose was totally concealed Pioneers of the Field Sir J C Bose’s Apparatus /

as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Prince of Mathematicians **Carl** **Friedrich** **Gauss** Himself known as the "prince of mathematicians“, referred to Mathematics as "the Queen of the Sciences ". This German /determination of the sides and angles of triangles. Trigonometry has now a wide application in higher Mathematics in **fact**, any attempt to study Higher Mathematics would be an utter failure without a working knowledge of trigonometry./

59/2, 206/7,..then simulate Saturn’s motion relative to Earth by making one gear with 7 teeth and one with 206 Gears Without Tears **Carl** **Friedrich** **Gauss** (1777-1855) Probability and Continued Fractions Any infinite list of numbers defines a unique real number by its cfe There can’t be a / 1/n K= 2.68545….. as n K k=1 {1+1/k(k+2)} ln(k)/ln(2) : Khinchin’s constant Captures the **fact** that the cfe entries are usually small e = 2.718.. is an exception (k 1........k n ) 1/n = [2 N/3 (N/3)!] 1/N 0/

and every good philosopher is at least half a mathematician.” **Friedrich** Ludwig Gottlob Frege www.ELATestPrep.com Think Like a Mathematician “God does arithmetic.” **Carl** **Friedrich** **Gauss** www.ELATestPrep.com Think Like a Mathematician "Where there is matter/Extended Thinking www.ELATestPrep.com Webb’s Definition of DOK (Hess, 2009) DOK-1 (Recall & Reproduction) Recall of a **fact**, term, principle, concept; perform a routine procedure; locate details DOK-2 (Basic Application of Skills/Concepts) Use of information;/

Supreme Court ex-associate justice What Is Intuition? **Carl** **Friedrich** **Gauss**’ Description 當高斯提到，如何解答一個長期困擾他的問題時，他 說：「就像是一道閃電一般，答案突如其來地，就把 問題自動解決。至於答案跟我本來就擁有的知識，有 何關聯，連我一時也說不上來。」 In referring to a long-standing problem which he had just solved, **Gauss** said, “Like a sudden flash of lightning, /is. u Explain why the creator often had no awareness of how a discovery had been made, even after the **fact**. u Explain why a discovery often occurred suddenly: Eureka! “Aha” phenomenon. AI Interpretation of Simonton’s Model /

fusion Modern statistics was founded by the German mathematician and astronomer **Carl** **Friedrich** **Gauss** (1777-1855). Prior to his work scientists often hand picked the “best” data points to derive the “most accurate” results. **Gauss** showed that the most robust and fair minded conclusions can be obtained/ in scientific notation represented as n.nnnn X 10 A the digits “n” arent necessarily the same number, but the **fact** that there are 5 of them means that a number such as 2.9979 X 10 8 has 5 significant figures. A/

asymptotically Family of Bachmann–Landau notations At most At least between absolutely Multiplication The mathematician **Carl** **Friedrich** **Gauss** (17771855) once noticed that although the product of two complex numbers (a + bi)(c + di) = ac-bd + (bc + ad)i seems to involve four real-number multiplications, it can in **fact** be done with just three: ac,bd, and (a + b)(c + d), since bc/

negative) roots of an equation. Efforts continued through the 18 th century on the theory of equations. Then German mathematician **Carl** **Friedrich** **Gauss** in 1799 gave the first proof (in his doctoral thesis) of the Fundamental Theorem of Algebra which states that every polynomial/ proved, without referring to the types of object the members of G actually were. This was effectively proving a **fact** about any set G which had the distinguishing properties, thus producing many theorems for one proof. It is possible /

our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science. — **Carl** **Friedrich** **Gauss** (1777-1855) Why Science? I have a theory… Water causes cancer Only water causes cancer Not cigarettes… /supernatural phenomena science itself requires neither the acceptance nor the rejection of the supernatural Scientific Method Scientific “**facts**” and theories many scientific theories, initially, are often little more than guesses based on limited information/

and the Cylinder, Book I, Assumptions, "Of all lines which have the same extremities the straight line is the least." 4. **Carl** **Friedrich** **Gauss**, (1777 –1855). "The line in which lie all points that, during the revolution of a body (or part of space) about/(1861-1947) Frege’s concept of ‘analytic’ had a great influence on the foundations of so-called ‘analytic philosophy.’ In **fact** it motivated Russell and Whitehead to attempt to found all of mathematics upon logical principles. In 1903, the book had the more/

, phenotypes of individuals for a quantitative trait tend to be normally distributed MCB 140, 12-8-06 9 Central limit theorem **Carl** **Friedrich** **Gauss** If a variable is the sum of many independent variables, then its distribution will be normal: MCB 140, 12-8/140, 12-8-06 56 Broad heritability is NOT, repeat, Nancy, Oliver, Tango, a general characteristic of this trait. In **fact**, for a trait, heritability can be 0 (if no genetic variation exists). Note that broad heritability being equal to zero does NOT/

Know theory of the case, defined objectives of interview Know your interviewee –Position, status in industry, education, criminal record? –**Fact** witness or potential target? –Incrimination/immunity issues? Interview plan: outline, documents 78 Preparation for the Interview (cont’d) Limit /Squares (OLS) estimates values of α and the βs Not a new tool, going back in its origins to **Carl** **Friedrich** **Gauss** (1777-1855) OLS also provides tests of statistical significance (T-stats, F-stat) and goodness of fit measures /

, director ____________ comedy, silent cinema __________________ a little tramp __________ the greatest comic actor, knight __________________________ BR1- **Carl** **Friedrich** **Gauss** 2. His Appearance: a small black hat ______________ a small moustache ________________ very wide trousers and big shoes/machine. Our job was to feed a robot. Officially, we were preparing dashboard molds for foam injection. In **fact**, we were simply loading and unloading the machine for the robot, which injected the foam and then wiped /

Y – selling price) 3) Use Excel to create a “scatter diagram”… 1.20 Scatter Diagram… It appears that in **fact** there is a relationship, that is, the greater the house size the greater the selling price… Patterns of Scatter Diagrams… /random variable is given by: It looks like this: Bell shaped, Symmetrical around the mean … SHOW THE VIDEOS **Carl** **Friedrich** **Gauss** The Normal Distribution… Important things to note: The normal distribution is fully defined by two parameters: its standard deviation and /

were verifications, not falsifications. How Popper managed to fool them [believers in falsification] I shall never know.The **fact** that Popper’s philosophy survived for so long is a sociological mystery.If we follow the sceptics [Feyerabend], the/ to play any role in his mechanism of thought. Hadamard described the experiences of the mathematicians/theoretical physicists **Carl** **Friedrich** **Gauss**, Hermann von Helmholtz, Henri Poincaré and others as viewing entire solutions with “sudden spontaneousness”. The same /

VA each month. Under VAs current business policies, the expected cash flow (revenues less expenditures) each month are in **fact** $0. How did Poindexter arrive at these conclusions? What is the expected demand from FearUs? From Oops? A New/ to describe the concept of lhomme moyen (the average man), thus popularizing the notion of the bell-shaped curve. **Carl** **Friedrich** **Gauss** (1777-1855) used the normal distribution to describe measurement errors in geography and astronomy. Bernoulli Processes and the Binomial /

. The maligned man had in **fact** been standing in a puddle which had discharged the current Wireless Communication Popular in the early 19th century was the heliograph, which was invented in 1810 by the German mathematician **Carl** **Friedrich** **Gauss**. The heliograph sported two mirrors/ Butler upon the adoption of the two-third rule." It requires no small intellectual effort to realize that this is a **fact** that now is, and not one that has been. Baltimore is 40 miles from Washington. It is a most wonderful /

to stand for the ratio of a circles circumference to its diameter 19 th century mathematics became increasingly abstract **Carl** **Friedrich** **Gauss** did work on functions of complex variables, in geometry, and on the convergence of series 20 th century /mathematics become a major profession the scientific age led to specialization with hundreds of specialized areas in mathematics Some **fact** and figures of Maths difficulties Figures from the States show approximatly 6-7% of students show evidence of serious/

H2H2 CO 2, H 2 O H2H2 CO Oxidation by O Transfer Agent Always increase the complexity in order to justify failure Johann **Carl** **Friedrich** **Gauss** 1777 - 1855 1777 - 1855 Coal Gasification/ CO 2 absorption CO 2 Release / Fe 2 O 3 reduction FeO oxidation / /first set foot there. So, while some ideas being used by writers are fiction... there could be some basis in **fact**. Who knows…. CONCLUSION The combined impact of increased fossil fuel costs, environmental concerns, political instability has to accelerate the /

even within their range of authority oChanges are very, very small 4/7/08Atoms and Stars, Class 1212 **Fact**? (cont’d) So science offers practical certainty, but not philosophic certainty oAlso, scientific knowledge changes Does / oLed to “Uncertainty Principle” Irreducible uncertainty in our knowledge 4/7/08Atoms and Stars, Class 1255 Uncertainty Principle 1795 **Carl** **Friedrich** **Gauss** (college student) Also Uncertainty Principal 1927 Werner Heisenberg – cannot locate particle exactly 4/7/08Atoms and Stars, Class /

even within their range of authority oChanges are very, very small 4/9/07Atoms and Stars, Class 1215 **Fact**? (cont’d) So science offers practical certainty, but not philosophic certainty oAlso, scientific knowledge changes Does / oLed to “Uncertainty Principle” Irreducible uncertainty in our knowledge 4/9/07Atoms and Stars, Class 1239 Uncertainty Principle 1795 **Carl** **Friedrich** **Gauss** (college student) Also Uncertainty Principal 1927 Werner Heisenberg – cannot locate particle exactly 4/9/07Atoms and Stars, Class /

geometry in which, through a point not on a line, there is more than one line parallel to the given line ? **Carl** **Friedrich** **Gauss** (German) looked at the previous question, but did not publish his investigation. Nicolai Lobachevsky (Russian) produced the first published / same center as the sphere. Since any two great circles intersect, in this model, lines can never be parallel! In **fact** in this model, lines always intersect at two points!. But the horizontal circles on a sphere have no points in common,/

changes are too small to detect 11/24/08Atoms and Stars, Class 1212Atoms and Stars, Class 1212 **Fact**? (cont’d) So science offers practical certainty, but not philosophic certainty oAlso, scientific knowledge changes Does/Principle” Irreducible uncertainty in our knowledge 11/24/08Atoms and Stars, Class 1247Atoms and Stars, Class 1247 Uncertainty Principle 1795 **Carl** **Friedrich** **Gauss** (college student) Uncertainty called (“sigma”, LC Greek s) Also Uncertainty Principal 1927 Werner Heisenberg – cannot locate /

Goneid, AUC21 Exercise Prove the formula: either by mathematical induction or by following the insight of a 10year-old school boy named **Carl** **Friedrich** **Gauss** (1777–1855) who grew up to become one of the greatest mathematicians of all times. Prof. Amr Goneid, AUC22 (/for (int i = 1; i <= n; i++) s = s + pow (y,i) / **fact** (2*i); return s; } Prof. Amr Goneid, AUC25 Cosine Function Evaluation The number of arithmetic operations is evaluated as follows: **fact** (2*i ) uses one mult. + 2i mult. = 2i+1 pow(y,i) uses (i-/

gets efficient information about the data stored in the pattern. -1805 Adrien-Marie Legendre, a French mathematician, and **Carl** **Friedrich** **Gauss**, a German mathematician, applied regression to determine orbits of planets around the sun. The objective of the regression/finally “learn” relationships from data that allows subject matter professionals to understand what a relationship means. 9 More **Facts** on the History of Data Mining 1989 The term “Knowledge Discovery in Databases” is created by Gregory Piatetsky/

rational number. But, does the number line consist solely of rational numbers? Might there be some other kind of number lurking on the number line? 19 Odd **facts** (even ones too) If m is an even integer, then m = 2q for some integer q. If m is an odd integer, then m =/of as a pair of real numbers, so is 2-dimension- al, as was noted by: Caspar Wessel (1745-1818) Jean Robert Argand (1768-1822) **Carl** **Friedrich** **Gauss** (1777-1764) 48 The complex plane -2 -1 0 1 2 i i -i 2i -2i 2+i 2-i 49 is algebraically closed The /

al.: “this definition is not very appealing to a mathematician, since it is based on experimentation, and, in **fact**, implies unrealizable experiments (N )”. But a physicist can take this with some pragmatism –A frequentist model can/y) in f with inverse transformation –Transform of the n -D volume with jacobian: PDF Examples Luca ListaStatistical Methods for Data Analysis21 Gaussian distribution **Carl** **Friedrich** **Gauss** (1777-1855) Average = x = Variance = (x ) 2 = 2 Widely used mainly because /

high-school graduates. u The culprit might be teachers education for the K-12 system, as suggested by the **fact** that few college and university professors were graduate of teachers colleges; college teachers were spared. Anton Lawson’s popular / thought to make discoveries; it was a common occurrence that discoverers had no conscious awareness of their own visual thinking (**Carl** **Friedrich** **Gauss** was a notable example). u Galileo’s evidence, as interpreted by Lawson, was too weak to be convincing about Galileo/

(3,3) is a schematic indication of the **fact** that each value of y is normally distributed about the straight line. That is, the most probable value of y will fall on the line, but there is a finite probability of measuring y some distance from the line. Least-squares curve fitting **Carl** **Friedrich** **Gauss** in 1795 Least squares: y=kx+b straight line/

ratios can occur in monohybrid crosses (e.g., in a dominance series), then you tell us they occur in dihybrid crosses and are, in **fact**, a hallmark of epistasis. How can one tell the difference? MCB140 09-17-07 39 Fig. 3.18 MCB140 09-17-07 40 “… /. MCB140 09-17-07 56 Morgan, ch. 8 MCB140 09-17-07 57 Hermann Nilsson-Ehle MCB140 09-17-07 58 Central limit theorem **Carl** **Friedrich** **Gauss** If a variable is the sum of many independent variables, then its distribution will be normal: MCB140 09-17-07 59 Fig. 3.17/

by a non-zero constant 3.Replace a row by the sum of itself and a constant multiple of another row kshumENGG201313 **Facts**: Elementary row operations do not change the solution(s). (There is no loss, and no gain, of information.) /which is easier to solve. kshumENGG201317 Linear system in upper triangular matrix form can be easily solved by backward substitution **Carl** **Friedrich** **Gauss** kshumENGG201318 (1777~1855) The old Deutsche 10-Mark note Gaussian elimination Step 0: Write the linear system in matrix/

Oughtred in the 1400s. Srinivasa Ramanujan (INDIAN) – An equation means nothing to me unless it expresses a thought of God **Carl** **Friedrich** **Gauss** – I proved a theorem not by dint of painful effort but by the grace of God George Cantor, Blaise Pascal, John/ exist? Logic and the mathematical imagination has given a product of the mind a (palpable) reality of its own! ‘True **facts** about imaginary things’ 5-dimensional hypercube 9-dimensional hypercube What is a 248-dimensional object? The Lie group E8 In 2006, /

remained until his death Other **facts** about Euler’s life Loss of vision in his right eye 1738 By 1771 virtually blind in both eyes –(productivity did not suffer-still averaged 1 mathematical publication per week) Religious Mathematical Predecessors Isaac Newton Pierre de Fermat René Descartes Blaise Pascal Gottfried Wilhelm Leibniz Mathematical Successors Pierre-Simon Laplace Johann **Carl** **Friedrich** **Gauss** Augustin Louis Cauchy Bernhard/

even a primitive ribozyme is a complicated structure, requiring 165 base-pair molecules to be strung together in the right order. In **fact** 4 165 possible structures – most of which are not self replicators – could be made from the same starting ingredients. 4 /September 9, 2004 Earths magnetic field is fading. Today it is about 10 percent weaker than it was when German mathematician **Carl** **Friedrich** **Gauss** started keeping tabs on it in 1845, scientists say. How old is the earth? Moon-dust Space Dust The earth’s/

This type of distribution is known as a bell curve or a Gaussian distribution (named for German mathematician **Carl** **Friedrich** **Gauss**) KEY TERMS Symmetric distribution When the data values are evenly distributed about the mean Negatively or left-skewed distribution/ a population Sampling error The difference between the sample measure and the corresponding population measure due to the **fact** that the sample is not a perfect representation of the population PROPERTIES When all possible samples of a specific/

honorary degrees from the University of Dublin and the University of Oxford. “I can speak confidently to the **fact** of his being not only well-versed in the highest branches of mathematics, but possessed of original power for/pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research” Johann **Carl** **Friedrich** **Gauss** (German, 1777-1855) Accomplishments: Disquisitiones Arithmeticae- book on the number theory Wrote a dissertation on the fundamental theory /

org http://mrsvandyken.pbwiki.com/ kymn.vandyken@asd20.org http://mrsvandyken.pbwiki.com/ "Mathematics is the Queen of the Sciences." - **Carl** **Friedrich** **Gauss** What can happen on a 3 year journey 1.A few calculators to check out 2. One school wide projector with a /Right/Wrong Multiple Choice Open Response View of Quick Poll and Options Fastest Finger Shared at T 3 in Dallas Great for basic **facts**, multiple choice problems, and homework +5 Being the first person and right +3 (if the 1 st person is not correct/

DAX Div-DAX 32 "The use leads the Sharpe reason to extraordinary results, however, which is owed to only the **fact** in truth that in connection with hedge funds all risks are not included with the volatility. Said differently the overall risk / changes (Downside deviation) are divided by 34 On the right steepness On the left crookedness 35 Discount - Certification 36 **Carl** **Friedrich** **GAUSS** 37 38 "Pre investment analysis always should of one and a hedge fund investment of a post investment risk management is/

O(N2 N ). Ring of possibilities Is there a Θ bound? 15 Lecture 22: Classy Complexity Classes Getting a Tighter Bound Johann **Carl** **Friedrich** **Gauss**, 1777-1855 gaussSum(n) = (n + 1)(n/2) What is the fastest known multiplication algorithm? Until 2007: Schönhage-/ remain a TM. The brain, however, is a muscle that is influenced by many factors, including usage. In **fact**, even the eldest of living humans can avoid mental breakdown by simply exercising their brains frequently… Christopher Andersen Note: exercising/

The method of elimination can be applied to a system of linear equations in more than two variables. In **fact**, this method easily adapts to computer use for solving linear systems with dozens of variables. When elimination is / each of which is obtained by using one of the three basic row operations. This process is called Gaussian elimination, after the German mathematician **Carl** **Friedrich** **Gauss**. 13 Example 3 – Using Gaussian Elimination to Solve a System Solve the system of linear equations. x – 2y + 3z = 9/

.edu MTH55_Lec-14_sec_3-3a_3Var_Sys_Apps.ppt 35 Bruce Mayer, PE Chabot College Mathematics Example Missing Term Translate: This geometric **fact** about triangles provides one equation: A + B + C = 180. B = 3A Angle B is three times /.edu MTH55_Lec-14_sec_3-3a_3Var_Sys_Apps.ppt 50 Bruce Mayer, PE Chabot College Mathematics All Done for Today **Carl** **Friedrich** **Gauss** BMayer@ChabotCollege.edu MTH55_Lec-14_sec_3-3a_3Var_Sys_Apps.ppt 51 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical/

that several informal but direct contacts have been made with political representatives of the viet cong in moscow Attack with frequency information 33 A countermeasure by **Carl** **Friedrich** **Gauss** Homophones The number of symbols assigned to each letter is proportional to the relative frequency of that letter. The letter e ⇒ 16/Alternatively, a message can be first encrypted and then hidden using steganography Advantage of steganography To lose the **fact** of parties of secret communication be discovered

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