L. RadhakrishnaUGC Centre for Advanced StudiesBANGALORE UNIVERSITY

1. EXHORTATIONS2. BISOCIATION & RESEARCH3. PROFESSIONAL

MATHEMATICAL WRITING4. CONCLUSION: ENHANCE

SCI

1. EXHORTATIONS:

Respect traditions & dignity of English:

i.Abbreviations

Dr Prof. Dept Rsii. Theorem of Euler’s.

SCIENCE PROTOCOL 2009 Jan 28

BUSINESS PROTOCOL Jan 28 2009

ARMYPROTOCOL 28 Jan 2009

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 20th Century“/ “The Most Creative Intellect in the Human Race” for just “Albert Einstein”.

[WONDER - JOY ] Hour.

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

2. RESEARCH &

Foundational approachFoundational approach: STANDARD PHILOSOPHIES IN MATHSSTANDARD PHILOSOPHIES IN MATHSFORMALISM (Hilbert)PLATONISM/ REALISM (Einstein)INTUITIONISM/ CONSTRUCTIVISM (Brouwer)

Mainstream approachMainstream approach: (Latest philosophy)MATHEMATICAL HUMANISM (Hersh 2001)

PHIL. MEANINGfulness INFALlibility GOAL

FORMALISM meaningless infallible invent [Pure]PLATONISM meaningful infallible discover [Applied]INTUITIONISM meaningfulfallibleconstruct in a finite number of steps [computer science] HUMANISM meaningful fallible

correctible

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.

c : c : CelerityCelerity (speed of light) (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 Continuumc : 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)]

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 = # { 𝑥 : 𝑥 is a real number} [Uncountable infinity]

‘The 20th century has transformedmathematics 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 PhysWW – III ?

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, MWriting Successfully in Science,

Chapman and Hall 1993

3. PROFESSIONAL 3. PROFESSIONAL MATHEMATICAL WRITINGMATHEMATICAL WRITING

Ramanujan is called the The Mathematician’s MathematicianThe Mathematician’s Mathematicianfor 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.

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

WRITE Mathematics RIGHT:

A Handbook for Professionals

L.Radhakrishna(to appear 2009)

Principles of Professional Writing: 250 [overcoming the challenge]

Euphony, Etiquettes & Elegance [desiderata of style]

Presentation format:Casual Professional Principle ofWriting Writing Professionalism

4. CONCLUSION:4. CONCLUSION:

An index of research professional

status: SCI ENCE CITATION

INDEX (SCI) 2000 For a 100- citation

3: 20,000 for India80: 20,000 the world average.

Bisociation for content Professionalism for form in reporting research as advocated by

Prof. V.V. Narlikar,the Professional Presenterwould help in boosting our SCI.

If IAGRG can enhance SCI better and it would not, then that is SIN!!

4.MATHEMATICIAN S &4.MATHEMATICIAN S &

dxe ∞

-x2

-∞

Who is a Who is a MathematicianMathematician??

Physicists are getting NOBEL prizes as well as FIELDS MEDALS.

Watch out ICM-2010 (Hyderabad)

India Mathematics Year-2009 (Delhi).

5. EIN5. EINSTSTEIN, EIN, GR, GR, IAGRG,SINP:IAGRG,SINP:

EIN ST EIN [ IJ GRG - Bern, 1986]

EINSTEIN is a correction to NEW TON F = ma + (F⋅u)u /c2 [Royal Society of London, 1984

Feb 9]

EINST EIN First one to create a subject without

historyThe happiest Thought : The happiest Thought : curvature of spacetime = curvature of spacetime =

GravitationGravitationGR is created entirely by one person!e-jl: Radhakrishna L., Mathematics Thrillerium, SUTRA: An International Jl of Mathematical Sciences

Education, Vol.1, 1-8, 2008http://www.tmrfindia.org/sutra/issue.html

WORLD 1 : PHYSICAL WORLDWORLD 1 : PHYSICAL WORLDmass, energy, stars, rocks, blood,

bone. WORLD 2 : INDIVIDUAL WORLDWORLD 2 : INDIVIDUAL WORLD

thoughts, emotions, awareness. WORLD 3: SOCIAL WORLDWORLD 3: SOCIAL WORLD

traditions, language, institutions [SINP],

conferences [IAGRG], mathematics

[[non-material culturenon-material culture]]

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).