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L. Radhakrishna UGC Centre for Advanced Studies BANGALORE UNIVERSITY

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1. EXHORTATIONS 2. BISOCIATION & RESEARCH 3. PROFESSIONAL MATHEMATICAL WRITING 4. CONCLUSION: ENHANCE SCI

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1. EXHORTATIONS:

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Respect traditions & dignity of English: i.Abbreviations Dr Prof. Dept Rs ii. T heorem of Euler’s.

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SCIENCE PROTOCOL 2009 Jan 28 BUSINESS PROTOCOL Jan 28 2009 ARMYPROTOCOL 28 Jan 2009

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Start with “The Climax in Elegance in Algebra” for the syllabus topic “ The Galois Group of a Field”. Start with “The Icon of the Millennium” / “The Person of the 20 th Century“/ “ The Most Creative Intellect in the Human Race” for just “Albert Einstein”. [WONDER - JOY ] Hour.

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Age, property are countable, but not important. Excellence, Enthusiasm, Guidance (personal or professional ) are not countable in units, but they count a lot for a research scholar.

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2. RESEARCH &

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Foundational approach Foundational approach : STANDARD PHILOSOPHIES IN MATHS FORMALISM (Hilbert) PLATONISM/ REALISM (Einstein) INTUITIONISM/ CONSTRUCTIVISM (Brouwer) Mainstream approach Mainstream approach : (Latest philosophy) MATHEMATICAL HUMANISM (Hersh 2001)

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PHIL. MEANINGfulness INFALlibility GOAL FORMALISM meaningless infallible invent [Pure] PLATONISM meaningful infallible discover [Applied] INTUITIONISM meaningfulfallible construct in a finite number of steps [computer science] HUMANISM meaningful fallible correctible

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BISOCIATION occurs when two seemingly unrelated things are shown to have unanticipated connections. Quantum field theory & Topology of 4D diff. manifolds; K-theory, Diff.Geometry & Elliptic PDE; Wavelets & Data analysis [genomics], Quantumgravity.

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c : Celerity (speed of light) c : Celerity (speed of light) (1) c + c = c [Einstein’s result 1905] where + : composition of collinear high speeds. Recall: In real analysis, c : Cardinality of the Continuum c : Cardinality of the Continuum (2 ) c + c = c [Cantor’s result, 1875] where + : the cardinal addition. The form similarity of (1),(2) is BISOCIATION. [c finite in(1) and c infinite in (2)]

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The potential (incomplete) infinity: ∞ An infinity of actual (completed) infinities: 0, 1, 2, ⋯. [Cantor’s paradise] A relation: 0 = # { 2, 4, 6, …, to ∞ }. = Cardinal number of the set of all natural numbers [Countable infinity] 1 = # { : is a real number} [Uncountable infinity]

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‘The 20 th century has transformed mathematics from a cottage industry run by a few semi-amateurs into a world-wide industry run by an army of professionals.' ATIYAH (WMY-2000) WW – I Chy, WW – II Phys WW – III ?

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ETHICS IN RESEARCH: “Ask permission from the copyright holder when you want to reproduce a complete table or figure or quote more than, say 100 words or 5% of the original publication, whichever is less”. Beware of ‘cut & paste culture’. O’Connor, M Writing Successfully in Science, Chapman and Hall 1993

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3. PROFESSIONAL MATHEMATICAL WRITING

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Ramanujan is called the The Mathematician’s Mathematician The Mathematician’s Mathematician for 600 conjectures ! - NEWMAN in M.Klein (Ed.) Math in the Modern World, 1969. Now Ramanujan’s work is applied to Computer Science, Cancer research and Polymer chemistry.

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Challenge 2005 “Although technical writing like teaching is a primary activity of many mathematicians, the principles of good mathematical exposition are rarely made explicit”. Boas, R.P. Editor, Notices of AMS

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WRITE Mathematics RIGHT: A Handbook for Professionals L.Radhakrishna (to appear 2009)

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Principles of Professional Writing: 250 [overcoming the challenge] Euphony, Etiquettes & Elegance [desiderata of style] Presentation format: Casual Professional Principle of Writing Writing Professionalism

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4. CONCLUSION:

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An index of research professional status: SCI ENCE CITATION INDEX (SCI) 2000 For a 100- citation 3: 20,000 for India 80: 20,000 the world average.

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Bisociation for content Professionalism for form in reporting research as advocated by Prof. V.V. Narlikar, the Professional Presenter would help in boosting our SCI. If IAGRG can enhance SCI better and it would not, then that is SIN!!

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4.MATHEMATICIAN S &

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∞ -x2-x2 -∞-∞ Who is a Mathematician ?

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Physicists are getting NOBEL prizes as well as FIELDS MEDALS. Watch out ICM- 2010 (Hyderabad) India Mathematics Year-2009 (Delhi).

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5. EINSTEIN, GR, IAGRG,SINP:

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EIN ST EIN [ IJ GRG - Bern, 1986] EIN STEIN is a correction to NEW TON F = ma + (F ⋅u)u /c 2 [Royal Society of London, 1984 Feb 9]

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EINST EIN First one to create a subject without history The happiest Thought : curvature of spacetime = Gravitation curvature of spacetime = Gravitation GR is created entirely by one person! e-jl: Radhakrishna L., Mathematics Thrillerium, SUTRA: An International Jl of Mathematical Sciences Education, Vol.1, 1-8, 2008 http://www.tmrfindia.org/sutra/issue.html

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WORLD 1 : PHYSICAL WORLD mass, energy, stars, rocks, blood, bone. WORLD 2 : INDIVIDUAL WORLD thoughts, emotions, awareness. WORLD 3: SOCIAL WORLD traditions, language, institutions [SINP], conferences [IAGRG], mathematics [ non-material culture ]

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Chaundy et al (1954), Halmos (1970), Steenrod, Schiffer, Halmos and Dieudonne (1973), Knuth et al (1987),Higham (1998), Krantz (1998), Swanson et al (1999), Maddox (2002).

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