Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
• Combinatorics
• Logic
• Number theory

Applied mathematics

• Dynamical systems and differential equations
• Mathematical physics
• Computing
• Information theory and signal processing
• Probability and statistics
• Game theory
• Operations research

Related Topics

• Electromagnetic Spectrum
• Linear Equations
• Applied Physics
• Nano Technology
• Engineering Sciences
• Mathematical Medicine
• Fluid dynamics
• Computational Mathematics
• Gamma Ray Optics
• Onfrared Optics
• Relative Velocity
• Iciam
• Intelligent Imaging Neuroscience
• Biomedical Engineering
• Neuroscience Research
• Quantum Cosmology
• Brain Research

• 4-manifold
• A Wrinkle In Time
• Alan E. Nourse
• Albert Einstein
• Algebra over a field
• Algebraic set
• Angle
• Arrow of time
• Arthur Cayley
• ArXiv
• Bernhard Riemann
• Bibcode
• Boundary (topology)
• C-symmetry
• Calabi–Yau spaces
• Cardinality
• Category Dimension
• Classical mechanics
• Clifford A. Pickover
• Commutative ring
• Complex number
• Configuration space
• Conformal geometry
• Connectedness
• Coordinates
• Cross-polytope
• Cube
• Cylinder (geometry)
• Demihypercube
• Dimension
• Dimension table
• Dimensional analysis
• Edwin A. Abbott
• Entropy
• Euclidean space
• Euler angles
• Exterior dimension
• Extra dimensions
• Flatland
• Fractal
• Fractal dimension
• Function space
• General relativity
• Geometric algebra
• Geometric topology
• Graph (mathematics)
• Habilitationsschrift
• Hausdorff dimension
• Henri Poincaré
• Higher dimensions
• Hilbert space
• Homeomorphic
• Hurst exponent
• Hypercube
• Hyperplane
• Hyperrectangle
• Hyperspace
• Hyperspace (book)
• Immanuel Kant
• Inductive dimension
• Integer
• Intrinsic dimension
• Isolated point
• Kaluza–Klein theory
• Knot (mathematics)
• Krull dimension
• Lagrangian mechanics
• Latitude
• Line (geometry)
• Line (mathematics)
• Linear algebra
• Linear combination
• Locally
• Longitude
• Ludwig Schläfli
• Lyapunov dimension
• M-theory
• Madeleine L'Engle
• Manifold
• Mass
• Mathematical object
• Mathematics
• Metric space
• Michio Kaku
• Miles J. Breuer
• Minkowski dimension
• Minkowski space
• Multiverse
• Murray Leinster
• N-dimensional space
• N-sphere
• Number line
• Octonion
• Open cover
• Orthonormal basis
• Parity (physics)
• Physics
• Plane (mathematics)
• Plane of rotation
• Planes of existence
• Platonic solid
• Poincaré conjecture
• Point (geometry)
• Pointwise dimension
• Polar coordinate
• Polytope
• Poset dimension
• Prime ideal
• Project Gutenberg
• Projective space
• Q-dimension
• Quantum field theory
• Quantum mechanics
• Quaternion
• Quaternions
• Real number
• René Descartes
• Robert A. Heinlein
• Rudy Rucker
• Science fiction
• Shlomo Havlin
• Simplex
• Space
• Space (mathematics)
• Space-filling curve
• Spacetime
• Special relativity
• Sphere
• Square (geometry)
• Stereoscopy
• String theory
• Structure
• Superstring theory
• Surface
• T-symmetry
• Tangent space
• Tesseract
• Thomas Banchoff
• Time
• Unit circle
• Vector space
• Volume
• William Sleator
• 
  

• 
  Albert Einstein
  Albert Einstein ( /ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪnʃtaɪn] ( listen); 14 March 1879 – 18 April 1955) was a German theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics. While best known for his mass–energy equivalence formula E = mc² (which has been dubbed "the world's most famous equation"), he received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect". The latter was pivotal in establishing quantum theory within physics.
  Near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led to the development of his special theory of relativity. He realized, however, that the principle of relativity could also be extended to gravitational fields, and with his subsequent theory of gravitation in 1916, he published a paper on the general theory of relativity. He continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the thermal properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the general theory of relativity to model the structure of the universe as a whole.
  
  wn.com/Albert_Einstein
• 
  Arthur Cayley
  Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician. He helped found the modern British school of pure mathematics.
  As a child, Cayley enjoyed solving complex math problems for amusement. He entered Trinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well as mathematics. He worked as a lawyer for 14 years.
  He postulated the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3. He was the first to define the concept of a group in the modern way—as a set with a binary operation satisfying certain laws. Formerly, when mathematicians spoke of "groups", they had meant permutation groups.
  See also Cayley's theorem.
  Arthur Cayley was born in Richmond, London, England, on 16 August 1821. His father, Henry Cayley, was a distant cousin of Sir George Cayley the aeronautics engineer innovator, and descended from an ancient Yorkshire family. He settled in Saint Petersburg, Russia, as a merchant. His mother was Maria Antonia Doughty, daughter of William Doughty. According to some writers she was Russian, but her father's name indicates an English origin. His brother was the linguist Charles Bagot Cayley. Arthur spent his first eight years in Saint Petersburg. In 1829 his parents were settled permanently at Blackheath, near London. Arthur was sent to a private school. He early showed great liking for, and aptitude in, numerical calculation. At age 14 he was sent to King's College School. The school's master observed indications of mathematical genius and advised the father to educate his son not for his own business, as he had intended, but to enter the University of Cambridge.
  
  wn.com/Arthur_Cayley
• 
  Bernhard Riemann
  Georg Friedrich Bernhard Riemann [ˈʁiːman] ( listen) (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting contributions to analysis, number theory and differential geometry, some of them enabling the later development of general relativity.
  Riemann was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is the Federal Republic of Germany today. His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars. His mother, Charlotte Ebell, died before her children had reached adulthood. Riemann was the second of six children, shy, and suffered from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as fantastic calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.
  During 1840, Riemann went to Hanover to live with his grandmother and attend lyceum (middle school). After the death of his grandmother in 1842, he attended high school at the Johanneum Lüneburg. In high school, Riemann studied the Bible intensively, but he was often distracted by mathematics. His teachers were amazed by his adept ability to solve complicated mathematical operations, in which he often outstripped his instructor's knowledge. In 1846, at the age of 19, he started studying philology and theology in order to become a priest and help with his family's finances.
  
  wn.com/Bernhard_Riemann
• 
  Henri Poincaré
  Jules Henri Poincaré (29 April 1854 – 17 July 1912) (French pronunciation: [ˈʒyl ɑ̃ˈʁi pwɛ̃nkaˈʁe]) was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
  As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002–2003. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.
  Poincaré made clear importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853–1928) in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity.
  
  wn.com/Henri_Poincaré
• 
  Immanuel Kant
  Immanuel Kant (German pronunciation: [ɪˈmaːnu̯eːl ˈkant]; 22 April 1724 – 12 February 1804) was a German philosopher from Königsberg (today Kaliningrad of Russia), who researched, lectured, and wrote on philosophy and anthropology during the Enlightenment at the end of the 18th century. At the time, there were major successes and advances in the sciences (for example, Isaac Newton, Carl Friedrich Gauss, and Robert Boyle) applying reason and logic.
  Kant’s major work, the Critique of Pure Reason (Kritik der reinen Vernunft, 1781), aimed to unite reason with experience to move beyond what he took to be failures of traditional philosophy and metaphysics. He hoped to end an age of speculation where objects outside experience were used to support what he saw as futile theories, while opposing the skepticism of thinkers such as Descartes, Berkeley and Hume.
  He stated:
  Kant proposed a ‘Copernican Revolution’ in reverse, saying that:
  Kant published other important works on ethics, religion, law, aesthetics, astronomy, and history. These included the Critique of Practical Reason (Kritik der praktischen Vernunft, 1788) and the Metaphysics of Morals (Die Metaphysik der Sitten, 1797), which dealt with ethics. And the Critique of Judgment (Kritik der Urteilskraft, 1790), which looks at aesthetics and teleology. He aimed to resolve disputes between empirical and rationalist approaches. The former asserted that all knowledge comes through experience; the latter maintained that reason and innate ideas were prior. Kant argued that experience is purely subjective without first being processed by pure reason. He also said that using reason without applying it to experience only leads to theoretical illusions. The free and proper exercise of reason by the individual was both a theme of the Enlightenment, and of Kant's approaches to the various problems of philosophy.
  
  wn.com/Immanuel_Kant
• 
  Ludwig Schläfli
  Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss geometer and complex analyst (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces. The concept of multidimensionality has since come to play a pivotal role in physics, and is a common element in science fiction.
  Ludwig you spent most of his life in Switzerland. He was born in Grasswil (now part of Seeberg), his mother's hometown. The family then moved to the nearby Burgdorf, where his father worked as a tradesman. His father wanted Ludwig to follow in his footsteps, but Ludwig was not cut out for practical work.
  In contrast, because of his mathematical gifts, he was allowed to attend the Gymnasium in Bern in 1829. By that time he was already learning differential calculus from Abraham Gotthelf Kästner's Mathematische Anfangsgründe der Analysis des Unendlichen (1761). In 1831 he transferred to the Akademie in Bern for further studies. By 1834 the Akademie had become the new Universität Bern, where he started studying theology.
  
  wn.com/Ludwig_Schläfli
• Michio Kaku
  Michio Kaku (加来 道雄, Kaku Michio^?, born January 24, 1947) is an American theoretical physicist, the Henry Semat Professor of Theoretical Physics in the City College of New York of City University of New York, a co-founder of string field theory, a futurist, and a "communicator" and "popularizer" of science. He has written several books about physics and related topics; he has made frequent appearances on radio, television, and film; and he writes extensive online blogs and articles. He has written two New York Times best sellers, Physics of the Impossible (2008) and Physics of the Future (2011). He has hosted several TV specials for BBC-TV, the Discovery Channel, and the Science Channel.
  Kaku was born in San Jose, California to Japanese immigrant parents. His grandfather came to the United States to take part in the clean-up operation after the 1906 San Francisco Earthquake^{[citation needed]}. His father was born in California but was educated in Japan and spoke little English. Both his parents were put in the Tule Lake War Relocation Center, where they met and where his two brothers were born.
  
  wn.com/Michio_Kaku
• 
  Murray Leinster
  Murray Leinster (June 16, 1896 - June 8, 1975) was a nom de plume of William Fitzgerald Jenkins, an award-winning American writer of science fiction and alternate history. He wrote and published over 1,500 short stories and articles, 14 movie scripts, and hundreds of radio scripts and television plays.
  Leinster was born in Norfolk, Virginia.
  He began his career as a freelance writer before World War I; he was two months short of his 20th birthday when his first story, "The Foreigner", appeared in the May 1916 issue of H. L. Mencken's literary magazine The Smart Set. Over the next three years, Leinster published ten more stories in the magazine. During and after World War I, he began appearing in pulp magazines like Argosy, Snappy Stories, and Breezy Stories. He continued to appear regularly in Argosy into the 1950s. When the pulp magazines began to diversify into particular genres in the 1920s, Leinster followed suit, selling jungle stories to Danger Trails, westerns to West and Cowboy Stories, detective stories to Black Mask and Mystery Stories, horror stories to Weird Tales, and even romance stories to Love Story Magazine under the pen name Louisa Carter Lee.
  
  wn.com/Murray_Leinster
• 
  René Descartes
  René Descartes (French pronunciation: [ʁəne dekaʁt]; Latinized form: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system — allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system — was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution and has been described as an example of genius.
  
  wn.com/René_Descartes
• 
  Rudy Rucker
  Rudolf von Bitter Rucker (born March 22, 1946) is an American mathematician, computer scientist, science fiction author, and philosopher, and is one of the founders of the cyberpunk literary movement. The author of both fiction and non-fiction, he is best known for the novels in the Ware Tetralogy, the first two of which (Software and Wetware) both won Philip K. Dick Awards. At present he edits the science fiction webzine Flurb.
  Rucker was born in Louisville, Kentucky. He is the great-great-great-grandson of the philosopher G. W. F. Hegel.
  Rucker attended St. Xavier High School before earning a B.A. in mathematics from Swarthmore College, and a Master's and Ph.D. in mathematics from Rutgers University.^{[citation needed]}
  Rucker taught at the State University of New York at Geneseo from 1972–1978. Thanks to a grant from the Alexander von Humboldt Foundation, Rucker taught math at the Ruprecht Karl University of Heidelberg from 1978–1980. He then taught at Randolph-Macon Women's College in Lynchburg, Virginia from 1980–1982, before trying his hand as a full-time author for four years. Inspired by an interview with Stephen Wolfram, Rucker became a computer science professor at San José State University in 1986, from which he retired in 2004. A mathematician with philosophical interests, he has written The Fourth Dimension; Geometry, Relativity and the Fourth Dimension; and Infinity and the Mind. Princeton University Press published new editions of Infinity and the Mind in 1995 and in 2005, both with new prefaces; the first edition is cited with fair frequency in academic literature.^{[citation needed]}
  
  wn.com/Rudy_Rucker
• 
  Shlomo Havlin
  Shlomo Havlin (born July 21, 1942) is a Professor in the Department of Physics at Bar-Ilan University, Ramat-Gan, Israel. He served as President of the Israel Physical Society (1996–1999), Dean of Faculty of Exact Sciences (1999–2001), Chairman, Department of Physics (1984–1988).
  Professor Shlomo Havlin was born in Jerusalem, Palestine (now Israel). He graduated from Bar-Ilan and Tel-Aviv Universities with Highest Distinction. He obtained an academic position at Bar-Ilan University in 1972 where he became a full Professor at 1984. During 1978–1979 he was a Royal Society Visiting Fellow at the University of Edinburgh, where he worked with Professors William Cochran and Roger Cowley. In 1984 he became the Chair of the Physics Department at Bar-Ilan University until 1988. During 1983–1984 and 1989–1991, Professor Havlin was a Visiting Scientist at NIH where he collaborated much with Drs. George Weiss, Ralph Nossal and other members of NIH. During 1984–1985 and 1991–1992 he was a Visiting Professor at Boston University, where he collaborated with Professor H. Eugene Stanley.
  
  wn.com/Shlomo_Havlin
• 
  Thomas Banchoff
  Thomas Francis Banchoff is an American mathematician specializing in geometry. He is a professor at Brown University, where he has taught since 1967. He is known for his research in differential geometry in three and four dimensions, for his efforts to develop methods of computer graphics in the early 1990s, and most recently for his pioneering work in methods of undergraduate education utilizing online resources.
  Banchoff received his Ph.D from UC Berkeley in 1964, where he was a student of Shiing-Shen Chern. Before going to Brown he taught at Harvard University and the University of Amsterdam.
  
  
  
  
  
  wn.com/Thomas_Banchoff
• William Sleator
  William Warner Sleator III (February 13, 1945 – August 3, 2011), known as William Sleator, was an American science fiction author who wrote primarily young adult novels but also wrote for younger readers. His books typically deal with adolescents coming across a peculiar phenomenon related to an element of theoretical science, then trying to deal with the situation. The theme of family relationships, especially between siblings, is frequently intertwined with the science fiction plotline.
  Due to the suspenseful and often eerie nature of some of his works, Sleator has been compared to young-adult horror writer R. L. Stine. Others cite a strong resemblance to the paranoid, dream-like style of Franz Kafka, which is most notable in House of Stairs, one of Sleator's more popular novels.
  Sleator was born in Havre de Grace, Maryland, the oldest of four siblings, to William Warner Sleator, Jr., a professor of physiology and biophysics, and to Esther Kaplan Sleator, a pediatrician who did pioneering research on attention deficit disorder (ADD). The Sleator family moved to suburban St. Louis, Missouri, when Billy, as the family called him, was three. His younger siblings are Vicky Wald, Tycho, and Daniel. He attended University City High School, where he was known as a composer who wrote scores for school plays and the orchestra, graduating in 1963.
  
  wn.com/William_Sleator

• Tree of Conscience
• Ancient Song
• Freedom Land
• Broken Heart
• Life
• Dreams
• The Next in Line
• Ego
• Egoman

• C'min Up
• If I Only Knew
• Into a New World
• Forever
• Seabird
• Rise
• When You're Gone
• Mosaique
• Place

• Double Market
• Black Street
• Se.le.ne
• Walkin'
• One and Three
• Yellow Sunshine
• Onozuka Solo
• Black Groove
• Colour Of Days

• Lazy Dog
• Head Games
• One and Three
• I Is 9th
• Close to Your Heart
• Jazz Cigarette
• Don't You Worry
• White of Blue
• Brighter in Your Life
• Yes or No?

• Cricket Smoker
• Double Vision
• Grey Jazz
• Bird Island
• Parable
• Parallel Words
• Leggy
• T.A Jingle
• Keep That Same Old Feeling

• Flip Out
• Se.le.ne
• Land Breeze
• Jungle Dancer
• Silver Rain
• No Reaction
• All For One
• Up Close
• Lull

• Break Out
• Aquarius
• Nothing Doing!
• Tones
• Safety Zone
• La-di-da Woman
• Blue Garden
• Aquatic Wall
• Colors of the Rainbow
• Autumn River

• Go Up Stream
• Take It Easy
• Throw Back
• After Fiver
• Child of Pirate
• Night Voices
• Ocean Express
• Selfcontrol
• NOIZ
• Rainy
• 薫風

• Q
• Sun Beam
• Harvest Moon
• Cyber Adventure
• Back For You
• M・S・F・B
• Head Hunter
• Asian Dream
• Black Groove
• Red Squeeze

• Double Market
• Black Street
• COLLAGE OF WATER
• Under the Word
• If
• Walkin'
• World order
• Impressions from the Outside
• Reflex
• L-MOTION
• WIGGLED OUT

• Magic One
• Key
• Someday
• Alone In Love
• Sundance
• Colour Of Days
• Moment
• I Don't Wanna Cry
• Shadow Of A Memory
• What's Rare?

• Hearts
• Stylish of Swing
• After Glow
• Mad About You
• Far Away
• Nudistic
• Changeover
• Do You Know Me?
• Hand Out
• Get With It
• Confusion

• Strategy
• Sailor
• Forbidden Game
• Universal Mind
• Waiting
• Vanity Calls
• Fearland
• The Mirror of Time
• Dimensional Gate

• timeline:
• 2012
• 2011
• 2010
• 2009
• 2008
• 2007
• 2006
• 2005
• 2004
• 2003
• 2002
• 2001

• timeline:
• 2012
• 2011
• 2010
• 2009
• 2008
• 2007
• 2006
• 2005
• 2004
• 2003
• 2002
• 2001