Euclid’s geometry is the first specific evidence of an axiomatic treatment of mathematics. Some 2000 years after Euclid, several mathematicians reexamined its axioms and discovered non-Euclidean geometry. One such geometry forms the space-time geometry of Einstein’s general theory of relativity. The discovery of non-Euclidean geometry was a revolution in mathematics, which led to what now forms the heart of mathematics—formal axiomatic systems. Formal systems form the basis of reasoning in mathematics and of all the computations we do on digital computers.

Several simple computations, as implemented on digital computers, will be examined. Their surprising common feature is that while there is no flaw in the coded logic, the computations fail. The reason for their failure and their remedies will be discussed. The lesson: programming is not about coding; it is about algorithms and their error propagation characteristics. We shall also take a look at some unusual ways humans prove mathematical propositions.

The notion of symmetry plays a central role in theoretical physics. The central theme of this lecture is the Emmy Nöther theorem, which states that for every observable symmetry in Nature there is a corresponding entity that is conserved. And for every conservation law there is a corresponding symmetry. For example, the law of conservation of angular momentum is a consequence of the isotropy of space. Quantum cryptography and quantum teleportation

The world of quantum mechanics is truly magical. In this lecture we will look at the basic mathematical framework around which QM is built, and then look at the amazingly simple solutions to two problems: (i) the safe exchange of keys for encrypted messages, and (ii) the teleportation of matter. In both these solutions, Charles Bennett, a distinguished IBM researcher, played a pioneering role.

The boldness with which Georg Cantor looked at the notion of infinity was a defining moment in mathematics. In a very real sense, he is the father of set theory. His proof that the set of real numbers is uncountable, and his proof that the set of points called the Cantor set is also uncountable and as numerous as the number of points on the real line are two remarkable examples of ingenious mathematical proofs. Of Cantor’s work on set theory, Hilbert was to say, “No one will drive us from the paradise that Cantor has created.” There were others who disagreed, Leopold Kronecker among them. The Cantor set plays an important role in non-linear dynamics and is a famous example of a fractal object.

In a competitive world where economic survival depends on being innovative, significant problems generally require beyond the state-of-the-art knowledge to find a solution. That is why competitive advantage devolves on societies which provide quality university education, foster well-complemented university-industry R&D collaborations, and are willing to welcome brains-in-circulation from anywhere in the world. Most people seem to forget that R&D and innovation are twin sisters.

Part I Copyright, trademark, trade secret
Some basic aspects of intellectual property rights related to copyright, trademark, and trade secret will be discussed. Patents will be discussed in the next lecture.

Part II Patent
This lecture will cover matters related to patentability, who can be named as an inventor in a patent, and ownership of patents. Important aspects related to the preparation of a patent application will also be discussed.

Part III Patent prosecution
Prosecution is the process by which a patent application is defended before the patent office before it takes a decision on the patent application. The process is both time consuming and rigorous. It typically consists of arguing in writing with an examiner about claims: over prior art, technical details, legal precedents, and claim language specifics. Important aspects related to patent prosecution will be discussed.

Part IV Infringement & litigation
Getting patents which will be found valid, enforceable and infringed when involved in patent infringement litigation are crucial. Infringed patents can be enforced through litigation; a patent is essentially the right to sue. Infringement and litigation is mainly about the power to regulate the manner in which goods and services are sold; it is not about the way people use those goods and services. Getting a patent and getting an enforceable patent are two different things. Important aspects related to infringement and litigation will be discussed.

Part V The ‘Bayh-Dole’ Acts
The Bayh-Dole Act of 1980 enacted in the U.S. in 1980 has been emulated by several other countries. After years of expectation, India too introduced a similar bill titled “Protection and Utilization of Public Funded Intellectual Property Bill 2008” in the Rajya Sabha on December 15, 2008. We examine the possible impact of the bill should it become law in light of experiences in the U.S. and Japan.

1. Bera, R. K., Method and system for processing of allocation and deallocation requests in a computing environment, Patent No. 8,195,802 (issued June 5, 2012).
2. Bera, R. K., Method, apparatus and computer program product for network design and analysis, Patent No. 8,176,108 (issued May 8, 2012).
3. Bera, R. K., Listing and modifying groups of blocks in the editing of a document, Patent No. 8,122,349 (issued February 21, 2012).
4. Bera, R. K., Run-Time parallelization of loops in computer programs using bit vectors, Patent No. 8,028,281 (issued September 27, 2011).
5. Bera, R. K., Compiler optimisation of source code by determination and utilization of the equivalence of algebraic expressions in the source code, Patent No. 8,028,280 (issued September 27, 2011).
6. Bera, R. K., Concurrent editing of a file by multiple authors, Patent No. 7,954,043 (issued May 31, 2011).
7. Bera, R. K., Restructuring computer programs, Patent No. 7,934,205 (issued April 26, 2011).
8. Bera, R. K., Determining the equivalence of two sets of simultaneous linear algebraic equations, Patent No. 7,836,112 (issued November 16, 2010).

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1. Rajendra K. Bera, The Amazing World of Quantum Computing, Springer Nature, Singapore, March 2020. https://link.springer.com/book/10.1007/978-981-15-2471-4
2. Bera, Rajendra K. Synthetic Biology, Artificial Intelligence, and Quantum Computing. Book Chapter in Synthetic Biology - New Interdisciplinary Science, Madan L. Nagpal, Oana-Maria Boldura, Cornel Baltă and Shymaa Enany, IntechOpen, DOI: 10.5772/intechopen.83434. https://www.intechopen.com/books/synthetic-biology-new-interdisciplinary-science/synthetic-biology-artificial-intelligence-and-quantum-computing
3. Bera, R. K., Synthetic Biology and Intellectual Property Rights, in Biotechnology (Deniz Ekinci, ed), InTech, ISBN 978-953-51-2040-7, Chapter 9, pp. 195-232 (2015), https://www.intechopen.com/download/pdf/48297. (Book is available at https://www.intechopen.com/books/biotechnology).
4. Bera, R. K., A novice looks at emotional cognition, arXiv:1304.5705 [cs.AI], 21 April 2013. https://arxiv.org/abs/1304.5705
5. Bera, R.K., and Menon, V., A new interpretation of superposition, entanglement, and measurement in quantum mechanics, arXiv:0908.0957v1 [quant-ph], 07 August 2009. https://arxiv.org/abs/0908.0957

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