Pure mathematics

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles. While pure mathematics has existed as an activity since at least ancient Greece, the concept was elaborated upon around the year 1900, after the introduction of theories with counter-intuitive properties (such as non-Euclidean geometries and Cantor's theory of infinite sets), and the discovery of apparent paradoxes (such as continuous functions that are nowhere differentiable, and Russell's paradox). This introduced the need to renew the concept of mathematical rigor and rewrite all mathematics accordingly, with a systematic

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Reducing Randomness in Matrix Models for Wireless Communication

Marc Desgroseilliers

Pushed by the proliferation of antennas and of multiuser scenarios, matrices with random entries are appearing more and more frequently in information theory. This leads to the study of matrix channels, where the capacity depends on the distribution of the matrix's eigenvalues. These eigenvalues are complicated functionals of the entries of the matrix and the challenge lies therein. It is often the case that in order to better model different communication scenarios, one is driven away from matrix models typically studied in pure mathematics and physics. One cannot simply resort to the standard tools developed over the years in these fields and must come up with new approaches. In this thesis, our goal is to obtain results in scenarios where the randomness is limited by the nature of the channel, in order to widen applicability in real life scenarios.

EPFL2015

Mathematics in the Wind

Nicola Parolini, Alfio Quarteroni

In any sport or human endeavor, coaches regularly state “play to your strengths.” One might not guess that a land-locked, mountainous country like Switzerland would have strengths that would give them a chance at winning the oldest, most competitive sailing competition in the world, the America’s Cup. But it does! In 2003, in the Harukai Gulf of New Zealand, a Swiss yacht called Alinghi was the surprise winner of the America’s up. And in 2007, in the Mediterranean sea near Valencia, Alinghi confirmed its dominance by defeating the New Zealand Team 5 to 2 in a breathtaking final match race. Mathematics and computational science were involved in Alinghi’s first successes in 2003, when it won the Louis Vuitton Cup and then the America’s Cup by defeating the defending Black Magic Team of New Zealand. Mathematics helped create the design of the boat which brought the defender Alinghi its second triumph in Valencia in 2007. Mathematical models were used in the design phase and again during the competition. Of course mathematical models alone are not enough to guarantee success in a race as competitive as the America’s Cup: a great team and much luck are needed. We know that people and explorers have been sailing literally since the stone age. It may seem astonishing that, with all the technological progress that has been achieved, sailing is still such a challenge. Alinghi has shown that part of the progress that will likely be made in the future rests on mathematical models and their numerical solution.

2009

A Simple, Robust, and Low-Cost Method To Produce the PURE Cell Free System

Barbora Lavickova, Sebastian Maerkl

We demonstrate a simple, robust, and low-cost method for producing the PURE cell-free transcription translation system. Our OnePot PURE system achieved a protein synthesis yield of 156 peg/mL at a cost of 0.09 USD/ktL, leading to a 14-fold improvement in cost normalized protein synthesis yield over existing PURE systems. The one pot method makes the PURE system easy to generate and allows it to be readily optimized and modified.

AMER CHEMICAL SOC2019

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