With the Prior Analytics, Aristotle is credited with the earliest study of formal logic, and his conception of it was the dominant form of Western logic until 19th century advances in mathematical logic.

With the development of fast Internet in the last part of the 20th century along with advances in computer controlled telescope mounts and CCD cameras ' Remote Telescope ' astronomy is now a viable means for amateur astronomers not aligned with major telescope facilities to partake in research and deep sky imaging.

With advances in medicinal chemistry, most of today's antibacterials chemically are semisynthetic modifications of various natural compounds.

With advances in aircraft design and equipment, they were joined by larger multi-engined biplane aircraft on both sides for long range strategic bombing especially by night.

With the continuing advances being made in the production of synthetic diamonds, future applications are beginning to become feasible.

With his advances in the atomic theory of matter, John Dalton devised his own simpler symbols, based on circles, which were to be used to depict molecules.

Following this, in 1985, Daniel Schacter proposed a more general distinction between explicit ( declarative ) and implicit ( procedural ) memory With the recent advances in neuroimaging technology, there have been a multitude of findings linking specific brain areas to declarative memory.

With advances in technology, the tone of horror films shifted from the Gothic towards contemporary concerns.

With the advent of the evidence-based medicine and great advances of information technology the process of change is likely to evolve further, with greater development of international projects such as the Human genome project.

With advances in the fields of molecular biology, biochemistry, nutritional immunology, molecular medicine and genetics, the study of nutrition is increasingly concerned

With the village being the grassroots ( usually a hundred or so families ), and not considered part of the hierarchy, local government advances through the township, county, prefecture or municipality, and the province as the geographical area of jurisdiction increases.

With phenomenal advances made in tool technology in the last two decades, it is the semiconductor industry view that excimer laser lithography has been a crucial factor in the continued advance of Moore ’ s Law, enabling minimum features sizes in chip manufacturing to shrink from 0. 5 micrometer in 1990 to 45 nanometers and below in 2010.

With the advances made in DASD technology, a read / write of a 4K record is just as efficient as a 1055 byte record.

With the phenomenal advances made in excimer laser photolithography tools by numerous researchers and companies, this trend is expected to continue into this decade for even denser chips, with minimum features reaching below 10 nanometers.

With the help of the Hungarians, Charles advances on Naples and captures Joan.

With Xerxes ' apparent acquiescence, Alexander seizes the Greek colony of Pydna and advances his frontiers eastward to the Strymon, taking in Crestonia and Bisaltia, along with the rich silver deposits of Mount Dysorus.

With today's technological advances, it is very easy for a producer to achieve high quality tracks without the use of a single instrument ; that happens in urban music ( like hip hop, rap, etc .).

With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor.

With advances in raw computer processing power, new products have appeared including NewTek's software application SpeedEdit.

With advances in molecular genetics, the mutant genes responsible for Arabidopsis thaliana genes ( GA 20-oxidase, ga1, ga1-3 ), wheat reduced-height genes ( Rht ) and

With advances in modern technology, cosmesis, the creation of lifelike limbs made from silicone or PVC has been made possible.

With new advances in detergents, lower water temperatures ( 50 – 55 ° C ) are needed to prevent premature decay of the enzymes used to eat the grease and other build-ups on the dishes.

With advances in these more sophisticated techniques, some of the more advanced crime scene investigation services from around the world were, as of 2010, reporting that 50 % or more of the fingerprints recovered from a crime scene had been identified as a result of laboratory-based techniques.

With advances in the fields of molecular biology, biochemistry, and genetics, the study of nutrition is increasingly concerned

With large sets, it becomes necessary to use more sophisticated mathematics to find the number of combinations.

With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.

With the advent of the BHK interpretation and Kripke models, intuitionism became easier to reconcile with classical mathematics.

Galileo maintained strongly that mathematics provided a kind of necessary certainty that could be compared to God's: " With regard to those few mathematical propositions which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty.

With the aid of standard mathematics, the classical spring system can be described in terms of vibrational modes, which are analogous to the harmonics that occur on a stretched violin string.

With the goal of founding all of mathematics on set theory, the group strove for utmost rigour and generality, creating some new terminology and concepts along the way.

With this view, the physical universe can thus be seen as the ultimate foundation of mathematics: it guided the evolution of the brain and later determined which questions this brain would find worthy of investigation.

With an assurance characteristic of the later sophists, he claimed to be regarded as an authority on all subjects, and lectured on poetry, grammar, history, politics, mathematics, and much else.

With traditional core competences in civil engineering, environment, transport, town and regional planning, mechanics, industrial management and logistics, École des Ponts ParisTech offers high-level programmes in an extensive range of fields, from applied mathematics to economics and management.

With the support of Weierstrass, this earned her a doctorate in mathematics summa cum laude, bypassing the usual required lectures and examinations.

With a definition of effective calculation came the first proofs that there are problems in mathematics that cannot be effectively decided.

With the goal of founding all of mathematics on set theory, the group strove for rigour and generality.

With her he studied natural philosophy and mathematics, and gave also great attention to languages, both ancient and modern, but soon abandoned them.

With the permission of the Lucasian professor, William Whiston, Saunderson was allowed to teach, lecturing on mathematics, astronomy and optics.

With the exception of Autolycus ' On the Moving Sphere, the Elements is one of the oldest extant Greek mathematical treatises and it is the oldest extant axiomatic deductive treatment of mathematics.

With disputes about the nature of mathematics, come questions about the nature of ethnomathematics, and the question of whether ethnomathematics is part of mathematics or not.

With the foundation of UNICAMP and the ready availability of high-quality researchers, engineers and students focused on physics, electrical engineering, computer sciences, mathematics, mechanical engineering, etc., a number of high-tech companies started to establish their industrial plants and R & D labs nearby, such as IBM.

With a fortune of about 80 000 livres Buffon set himself up in Paris to pursue science, at first primarily mathematics and mechanics, and the increase of his fortune.

With aspirations of helping people who lack full mobility, ASIMO is used to encourage young people to study science and mathematics.

With applications to mathematics, information theory and to the natural and social sciences.

With this course work, students will emerge from the core curriculum possessing a strong set of skills in reading, writing, oral communication, and mathematics.

With Kumazawa, he also discovered how to connect his interests in botany and mathematics: biometry.

With the rise of theoretical physics in the early part of the Twentieth Century and its foundation in mathematics, David Hilbert decided to lend an organizing hand to formalizing the sciences, starting with physics.