Abstract
This paper examines how, for many who lack a strong grounding in math and science, the two are often associated as being the same. The purpose of this paper is to define mathematics and science, showing them as two distinct fields of inquiry and then to show how advances in theoretical mathematics contribute the framework needed for scientists in the study of quantum mechanics, a branch of physics, which in turn, is one of the many branches of science.

Outline
Introduction
Mathematics
Science
Quantum Mechanics
Mathematics and Quantum Mechanics
Science and Quantum Mechanics

From the Paper
"Finally, applied mathematics is a term loosely applied to a range of studies which have significant use in the sciences, specifically the empirical sciences, (branches of science open to practical or experiential experimenting). Applied mathematics makes use of numerical methods and computer science, seeking concrete solutions to explicit mathematical problems. In science and technology it has a major use as a way to model and/or simulate natural phenomenon or events. Examples include using mathematical models in computer generated wind tunnel tests to predict the behavior of a given shape of a prototype airplane wing without resorting to expensive actual wind tunnel testing."

Tags:quantum, mechanics, technology

Abstract
This paper introduces and explains several theories in physics, such as the M theory, string theory, quantum mechanics, and general relativity theory. It presents them in layman's terms and explains how these theories all work (or don't work) together.

From the Paper
"Quantum mechanics or the quantum field theory has worked well to describe the known behaviors and properties of particles of the Planck length or very small particles. General Relativity works with large objects like planets and galaxies. However the theories only works when one of the two theories can be neglected. General relativity has explained a lot about the universe, the evolution of stars, the orbits of planets, and best-known theory "the Big Bang". It also shows how black holes and gravitational forces work. However, the General relativity theory only works on its own and when we think of the universe in traditional matter because of the fact that quantum mechanics dose not comply the description of General Relativity. The two work well to explain the theories they were set up to explain however the do not work together. String theory was then conceived to explain the how Quantum Mechanics, the really small stuff, and General Relativity, the really large stuff, works together."

Tags:einstein, field, general, mechanics, physics, quantum, relativity, string, theoretical, theory, unified

Abstract
This paper explains string theory, which has been put forth by physicists in an effort to develop a theory of gravity that can be incorporated into the quantum understanding of nature. The paper explains that string theory hypothesizes that classical point particles are actually infinitesimally small lines or, perhaps, loops and that the theory supports the concept that all quantum particles, including the messenger particle of gravity, or graviton, are components of a single, master superfield.

From the Paper
"Generally speaking, considering the enormous amount of matter that was concentrated in a tiny space after the Big Bang, the setting for unification is contained by almost unbelievable energy levels. Efforts to achieve this "mathematically" have been reasonably successful and are termed Grand Unified Theories, or GUT. So far, physicists have managed to unify the electromagnetic, weak, and strong interactions into one formalism."

Tags:fundamental, forces, nature, nuclear, force, unify, unification, big, bang, universe

Abstract
The paper discusses how Albert Einstein's scientific genius rendered him the most famous scientist of the 20th century but contends that his intense humanism probably resulted in his status as a cultural icon. The paper relates that it is sometimes not realized that Einstein lamented his breakthrough in relativity and the splitting of the atom that permitted the Allies to create the atomic bomb that ended World War II and heralded our nuclear age.

From the Paper
"Much rhetoric has been written on how scientific discoveries reshape a period and sometimes an entire culture. Gerald Holton notes that Einstein's scientific papers on relativity, statistical mechanics and quantum physics in the first two decades of the 20th century, "caused remarkable and sometimes quite unforeseen cultural transformations and resonances" (p. 125). Of course, Albert Einstein is credited with the theory of general relativity to revolutionize the sciences into the 21st century and the new orientation of relativity would strongly affect the social sciences, plus the world of arts and letters."

Tags:einstein, physics, philosophy

Abstract
This paper describes dark energy, or anti-gravity, and debates theories of universe expansion, touching on Einstein's theory of relativity and cosmological constant. It also talks about the equation of state of the universe and its impact on universe expansion or contraction. It looks at how there are many theories about dark energy from the quintessence theory and the topological defect theory to the cosmological constant theory. It explains that, by analyzing the equation of state of this energy and evaluating current theories, scientists can construe a plausible theory for the fate of the universe.

From the Paper
"Physicists started negotiating and theorizing about the possibility of a dark energy around the turn of the century. One generally un-disproved theory from that time is that which relates the equation of state to the "cosmological constant." The cosmological constant (often called lambda) was proposed by Einstein in 1917 to make the universe unchanging in his equations (5). He was generally unsure of this idea, and rejected this theory shortly after it was determined that the universe is perpetually growing. However, his idea of a cosmological constant is currently applied to the universe in a slightly different way, setting the equation of state constant (5)(4). The current theories of dark energy date back to 1998 when supernovae were discovered to be dimmer than expected."

Tags:cosmological, einstein, gravity, hubble, quintessence

Abstract
This paper discusses the work of the physicist John Bell, who's great recognized achievement occurred during the 1960s when he brought new life into the foundations of quantum theory. It examines how Bell demonstrated that discussion of such concepts as 'realism', 'determinism' and 'locality' could be formed into a rigorous mathematical statement, 'Bell's Theorem', which is capable of experimental test. It looks at how his work has become a point of interest for scientists throughout the world who have found applications not only in quantum theory, but in investigations of the physical universe as well and how current applications of Bell's Inequality have been found in the development of quantum computing and quantum cryptography.

From the Paper
"Quantum mechanics, however, fails to satisfy Bell's Inequality. He predicts correlations that cross over boundaries that are delineated by the structure of that inequality. Quantum mechanics predicts "odd" correlations that seem to defy a common, classical conception of reality, and in fact it is for basically this type of reason that Einstein, Podolsky, and Rosen argued in 1935 that it was incomplete. The formulation of Bell's Inequality, however, allowed the possibility for determining, through experiment, which was right: quantum mechanics or a local reality theory of the sort Einstein postulated, because it stated what must be the case in our experiments if a locally real theory is correct."

Tags:computing, cryptography, polarization, photon

Abstract
This essay explains the basis of Quantum Mechanic Theory of the atom, which describes the behavior of electrons in atoms & molecules. The author examines this theory and provides a detailed analysis of it.

From the Paper
"The Quantum Mechanics Theory describes the behavior of electrons in atoms & molecules. Quantum Mechanics is also referred to as Wave Mechanics. The theory of quantum mechanics tells us that in the atom, electron waves are standing waves. This theory was devised by Max Planck in 1901. He stated that light is emitted by the atoms of a luminous body in separate packets or bundles of energy called quanta or photons. One or more of the electrons revolving about the nucleus of an atom can be made to jump from one orbit to another. As they do so one or more photons are emitted. This energy radiates from the luminous body as electromagnetic waves. The energy content of a photon determines the length and frequency of the wave. Wave mechanics views the probability of finding an electron at a given point in space."

Tags:chemistry, physics

Abstract
The paper traces Einstein's formative years, focusing on the difficulties he encountered at school. The paper analyzes the way his Theory of Relativity affected many areas of life in Einstein's day, such as science, the arts and the production of weapons of mass destruction. It also examines the fact that since Einstein's theories have never been disproved, most modern scientific research is still based upon his theories.

From the Paper
"Einstein will likely be remembered for into the future for the scientific contributions he made, but it is important that those who steadily Einstein and admire his work also realize that he was an individual with thoughts and feelings of his own. He was generally a pacifist and a humanitarian who even renounced his German citizenship when the Nazis took over Germany. He came to the United States instead, and spent his days in New Jersey, where he continued to work on various scientific theories and other notable information. Albert Einstein passed away in 1955, and the scientific community suffered a great loss that day."

Tags:quantum, physics, gravitation, light, space, energy

Abstract
This paper deals with the two competing theories of light. The first part of the paper details the evidence supporting the theory of light as a particle, including both the most prominent scientists and the most conclusive mathematical data (Photoelectric effect, Compton Effect, etc.); the second part lists the evidence in favor of the wave theory of light, including prominent supporters and the most concrete scientific evidence (Young's double-slit experiment, Clark Maxwell's mathematical equations). The paper concludes by detailing the newest theory to encompass both the particle and wave theories.

Particle Theory
Einstein
Isaac Newton
Scientific Evidence
Photoelectric Effect
Compton Effect
Wave Theory
Huygens
Scientific Evidence
Young's Double-slit Experiment
Maxwell Clark's Mathematical Equations
The Dual Nature of Light

From the Paper
"If it is part of the material world, it is certainly, by dint of its surpassing subtlety, the part that is closest to the spirit, said Johannes Kepler in his description of light (Holt, 1). As elusive and mystical as the Almighty, light has been a companion, rivaled only by oxygen, to mankind since men first trod upon the earth, an eternal, comforting friend. It terrified and was deified by the men and women of religion; it fascinated and frustrated the theorists, the scientists, and countless cracks; and yet for both it offered an enigma to be solved, a question worthy of an answer. Thus, from the foothills of Classical Greece to the stone castles of Italy and Germany, humanity found itself hounded by a question seemingly so basic: What is light? This question remains only marginally answered at the end of this century, three millennia after the Greeks first hypothesized about the subject. Although centuries upon centuries of labor and experiments have led to millions of dusty binders and folders, only two camps ever gained the blessings of science in a quest for a solution: those who believed light to be a particle and those who believed it to be a wave. "

Tags:science, einstein, newton

Abstract
This paper expounds the "Theory of Everything," starting with the pioneering theories of Newton's "Laws of Motion" and Einstein's "General Theory of Relativity," developing right through to the cutting-edge "string theory" research currently being conducted around the world today. It shows the importance of fields of study as seemingly diverse as calculus, differential geometry, electromagnetism, particle physics and quantum mechanics to the development of a "Theory of Everything."

From the Paper
"However, there is a fundamental discord between Einstein's "Theory of General Relativity" and quantum mechanics. Einstein saw the universe in four dimensions (the three dimensions of space plus time). The gravitational force that binds matter to the earth stems from this space-time continuum. Since quantum mechanic's subatomic particles only exist theoretically, they cannot be located in space-time and their motion can only be hypothesized. Thus, we have two theories that work individually but not together. There are also many unanswered questions. Relativity cannot tell us how the big bang created the universe or what black holes consist of. Similarly, quantum theory is not able to make order or sense of the assortment of miniscule matter it describes."

Tags:calculus, differential, einstein, electromagnetism, geometry, gravity, mechanics, motion, newton, particle, physics, quantum, relativity, string