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## MATH 533 Heliocentric vs Geocentric Solar System Keplers Laws Essay

Order ID# 45178248544XXTG457Plagiarism Level: 0-0.5%Writer Classification: PhD competentStyle: APA/MLA/Harvard/ChicagoDelivery: Minimum 3 HoursRevision: PermittedSources: 4-6Course Level: Masters/University CollegeGuarantee Status: 96-99%

InstructionsMATH 533 Heliocentric vs Geocentric Solar System Keplers Laws Essay

Heliocentric vs. geocentric solar system, Keplers laws, Inductive reasoning and Galileo

Analytic geometry and deductive reasoning: Descartes and FermatWhat purpose does coordinate geometry have for Descartes, and what relationship does it have with geometric construction and problem-solving? How does it relate to his Method?

Indivisibles: Galileos paradoxes of the infinite, Cavalieris principle

Was there any work before Newton and Leibniz about finding equations of tangent and normal lines to curves? or about quadrature (areas under curves)? If so, why do we credit Newton and Leibniz with the discovery of calculus instead of Isaac Barrow and some of these other folks?

Isaac Newtons method of fluxions, fluents, moments

Newtons Principia MathematicaWhat is it about, why is it important, how does it differ from his earlier version of calculus with fluxions?

G.W. Leibnizs infinitesimalsHow are these different from indivisibles? How are they different from Newtons infinitesimals? What complaints do some contemporaries have about them?

Who are some folks who applied calculus ideas in the early 1700s and what is an example of how they did?

Why are power series important in the development of calc? Why was it important that Eulers work with infinite series and analysis was so formal and symbolic? How does this influence Lagranges development of calculus?

How does the idea of function change between 1700 and 1850?

Why does each of the following examples of 19th-century mathematics reflect a crisis of the Enlightenment perspective of the previous century? How did things not work quite so smoothly as previously thought? Examples:

o Fourierseries

o Insolvabilityof5th-degreepolynomials,andofthe3toughGreekconstructionproblems o Non-Euclideangeometry(whatisthis,whodowecreditwithitsdiscovery,andwhydoes

it reflect a change of perspective?)

o Infinitesimalsgetreplacedbylimits(when,bywho?)

What is set theory and how does it relate to the axiomatization of mathematics? Who are the characters in that story?

What are formalism, platonism, intuitionism, and logicism? More specifically:

o Whywereintuitionists(constructivists)opposedtoCantorsideasaboutinfinitesets? o Whatareacoupleimportantmathematicalideaswemightnothavehadifwewereall

platonists, and why?

o HowdoGødelsincompletenesstheoremschallengetheformalistprogram?

o Asaformalist,whydoesitmakesensethatHilbertthoughttheContinuumHypothesis

was an important question?

Chinese math examples: counting boards, number representations and calculation methods, systems of equations, magic squares, Pythagorean theorem, Chinese remainder theorem

Mayan math: calendars, pure base-20 system vs. positional almost-base-20 solar calendar system, zero

Inca math: what were quipus for, how were numbers represented, yupanas (weird abacuses) and calculation

RUBRIC

Excellent Quality95-100%

Introduction45-41 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Literature Support91-84 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Methodology58-53 points

Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.

Average Score50-85%

40-38 points

More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.

83-76 points

Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.

52-49 points

Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.

Poor Quality0-45%

37-1 points

The background and/or significance are missing. No search history information is provided.

75-1 points

Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.

48-1 points

There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met

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