09 SepMath Goes to the Movies

Burkard Polster and Marty Ross Johns Hopkins University Press, 2012, ISBN: 978-1-4214-0483-7 (hardback) Also available in paperback (ISBN: 978-1-4214-0484-4) and for Kindle   This is an entertaining grab bag of mathematical and movie titbits that will delight mathematically minded movie buffs. The authors also have a website that includes links to...

07 SepMathematical Quest 4: More about Primes

The following was published in Young NE, Vol. 1, Issue 5 (September 2013). We thank the editor of Young NE for permission to post this here.

05 SepAmazing Number Nine

IT IS VERY INTERESTING TAKE ANY NUMBER OF DIGITS. HERE I AM TAKING 25 AND 32
• YOU CAN WRITE THEM IN FOUR WAYS LIKE THAT(25*32/25*23/52*23/52*32)

25*32=800

25*23=575

52*23=1196

52*32=1664

• SUBTRACT BIGGER ONE TO ANY LOWER, ONE BY ONE

1664-1196=468=4+6+8=­18=1+8=9

1664-575=1089=1+0+8+­9=18=1+8=9

1164-800=864=8+6+4=1­8=1+8=9

1196-575=621=6+2+1=9

1196-800=396=3+6+9=1­8=1+8=9

800-575=225=2+2+5=9

Always THE SUM IS 9. IT IS TRUE FOR ANY DIGITS..

05 SepVideo Lecture on Numbers

The editor of the English section of this website gave a video lecture for school students of Podar International School in Mumbai. The video can be seen below. [ad#ad-2]...

26 AugTopological Fixed Point Theory

1. Introduction Fixed point theory is very simple, but is based on fundamentals in Mathematics. For any continuous function \$\$f:Xrightarrow X\$\$ a fixed point of \$\$f\$\$ is a point \$\$xin X\$\$ satisfying the identity \$\$f(x)=x.\$\$ Two fundamental theorems concerning fixed points are Banach Theorem and Brouwer Theorem. Banach theorem states that if \$\$X\$\$ is a complete metric space and \$\$f\$\$ is a contraction then \$\$f\$\$ has a unique fixed point. In Brouwer theorem, \$\$X\$\$ must be the closed unit ball in a Euclidean space. Then any \$\$f\$\$ has a fixed point. But in this case, the set of fixed points is not necessarily a one-point set. In Banach theorem, a metric on \$\$X\$\$ is used in the crucial assumption that \$\$f\$\$ is a contraction. The unit ball in a Euclidean space is also a metric space and the metric topology determines the continuity of continuous functions, however the essence of Brouwer theorem is a topological property of the unit ball, namely the unit ball is compact and contractible. Banach theorem and Brouwer theorem tell us a difference between two major branches of fixed point theory, metric space fixed point theory and topological fixed point theory. It is impossible to distinguish two fixed point theories in an exact way, and it is not easy to determine a certain topics belong to which branch. In general, the fixed point theory is regarded as a branch of topology. But due to deep influence on topics related to nonlinear analysis or dynamic systems, many parts of the fixed point theory can be considered as a branch of analysis.

26 AugApproximating Integrals in High Dimensions— An Informal Report

1. Introduction For half a century or more many researchers have grappled with the problem of numerical integration in many dimensions— on the one hand to understand what is possible, on the other to construct and analyse effective algorithms. This is an informal and rather personal...

26 AugAn Interview with Ian Sloan

September 3, 2012, in Sydney (Ian Sloan) and Singapore (Peter Hall)   Introduction. Ian Hugh Sloan was born in Melbourne on June 17, 1938, and educated at Scotch College, Melbourne, and Ballarat College, before going on to undergraduate degrees in physics and mathematics at the University of Melbourne. Shortly after completing his BSc and BA (Hons) in late 1960 he joined the Colonial Sugar Refining Company. This might sound like an inauspicious start for a research mathematician, but by the early 1940s, CSR, as it is called today, had already diversified into building products and chemicals, and by the late 1950s had plans for a future based largely on scientific research. Thus, Ian was able to undertake a PhD in theoretical atomic physics at University College, London while receiving a salary from CSR. However, when Ian returned to Australia in 1964 he found a changed CSR. In particular, the research project on which he was supposed to work had collapsed, and his employer was more focused on short-term, rather than long-term, goals. So he left, and joined the University of New South Wales in 1965, and has been there ever since. Over the ensuing 48 years he has developed and fostered Australia’s premier numerical analysis programme.

22 AugMathematics of Planet Earth (MPE) 2013

The following article appeared in the August 2013 issue of the magazine Young NE and is reproduced here with the permission of the editor of Young NE.

22 Augগণিত আৰু মানৱতাৰ এক তেঁজাল ঘোঁৰা এভাৰিষ্ট্ গেল্-ওৱা

পোনপ্ৰথমবাৰৰ বাবে বিশ্ববিদ্যালয়ৰ গণিত বিভাগত হৈ যোৱা ৰাষ্ট্ৰীয় সন্মিলনখনিক লৈ বিভাগৰ আটাইখিনি মানুহেই অতি ব্যস্ত হৈ আছিলোঁ, যদিওবা শ্ৰেণীকোঠাৰ দায়ীত্বৰ পৰা আঁতৰি আছিলোঁ। এই সুযোগতে জন ষ্টিলৱেলৰ স্প্ৰিংগাৰৰ পৰা প্ৰকাশিত ‘মেথেমেটিক্স এণ্ড হিষ্টৰী’ শীৰ্ষক কিতাপখনি হঠাতে হাতত পৰিল। কিতাপখনৰ পাতনিটো পঢ়ি ভাল লাগিল। লিখা আছিল—
‘One of the disappointments experienced by most mathematics students is that they never got a course of mathematics. They get course in calculus, algebra, topology, and so on. But the division of labor in teaching seems to prevent these different topics being combined into a whole.’
প্ৰথমতেই আকৃষ্ট হৈ পাত লুটিয়াই গ’লোঁ, এই কথা মনত ৰাখি যে, সাধাৰণ পাঠকক দিব পৰা কিবা আছে নেকি? তাৰেই এটা চেষ্টা এনেদৰে আগবঢ়াইছোঁ। আধুনিক শুদ্ধ বা বিমূৰ্ত গণিতৰ এটা শাখা ‘গ্ৰুপ-থিওৰি’ৰ ক্ষেত্ৰখনত এক অনন্য প্ৰতিভা ‘এভাৰিষ্ট গেল্-ওৱা’ৰ জীৱন কাহিনীনো কেনে উপন্যাসোপম তাকেই চাব খুজিছোঁ এই প্ৰবন্ধটিত। মাথোঁ একৈশ বছৰীয়া জীৱন এটাৰে জগতক দি থৈ গৈছে এক অভূতপূৰ্ব অৱদান। পেৰিচৰ ওচৰৰ এখন নগৰত জনম লৈছিল এইজনা ক্ষণজন্মা গণিতৰ নায়কে, ১৮১১ চনত। গেল্-ওৱা সম্পৰ্কত জন ষ্টিলৱেলৰ এক মনোমোহা টিপ্পনী— “যদিওবা গেল্-ওৱাৰ জীৱন সম্বন্ধে জনা কথাখিনিয়ে আমাৰ এক নাটকীয় পৰিবাসনা তৃপ্ত কৰে, পিছে এই ক্ষণজন্মা নাযকজনৰ ট্ৰেজেডিখিনি বেছি ‘ক্লাছিকেল’ ধৰণৰ, যাৰ বীজ নিহিত হৈ আছে ‘ভিক্টিম’ জনৰেই জীৱনৰ মাজত, অৰ্থাৎ ময়েই মোৰ ভাগ্যনিয়ন্তা।” গেল্-ওৱা আছিল গণিতৰ জগতৰ আটাইতকৈ ৰোমান্তিক ব্যক্তিত্বৰ।

09 AugApplications of Lie Groups to Difference Equations

Vladimir Dorodnitzy Chapman & Hall/ CRC, 2010, 344 pp.   The invariance of differential equations under transformation groups, usually Lie groups, naturally comes from the models they formalise, and there is a lot of literature dedicated to applications of Lie groups in differential equations. The difference schemes for...