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Emil Post
Emil Leon Post (; February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. Life Post was born in Augustów, Suwałki Governorate, Congress Poland, Russian Empire (now Poland) into a Polish Jews, Polish-Jewish family that immigrated to New York City in May 1904. His parents were Arnold and Pearl Post. Post had been interested in astronomy, but at the age of twelve lost his left arm in a car accident. This loss was a significant obstacle to being a professional astronomer, leading to his decision to pursue mathematics rather than astronomy. Post attended the Townsend Harris High School and continued on to graduate from City College of New York in 1917 with a B.S. in mathematics. After completing his Doctor of philosophy, Ph.D. in mathematics in 1920 at Columbia University, supervised by Cassius Jackson Keyser, he did a post-doctorate at Princeton University in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustów
Augustów is a town in north-eastern Poland. It lies on the Netta River and the Augustów Canal. It is the seat of Augustów County and of Gmina Augustów in the Podlaskie Voivodeship. Augustów has an area of , and as of June 2022 it has a population of 29,305. In 1970, Augustów became officially recognized as a health and relaxation (psychology), relaxation resort. In 1973, surrounding settlements were named a part of it, forming a popular resort town. History A settlement in the area was first mentioned in 1496. Augustów was established around 1540 by Bona Sforza and granted Magdeburg rights in 1557 by Sigismund II Augustus, after whom it was also named. It was laid out in a very regular manner, with a spacious market-place. Until 1569 Augustów belonged to the Grand Duchy of Lithuania. In 1569 it became part of the Crown of the Kingdom of Poland, while its cemetery was left in the Grand Duchy, both countries formed the Polish–Lithuanian Commonwealth as a result of the U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, A and B), and one final column showing all of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of the operation for those values. A proposition's truth table is a graphical representation of its truth function. The truth function can be more useful for mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Ponens
In propositional logic, (; MP), also known as (), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "''P'' implies ''Q.'' ''P'' is true. Therefore, ''Q'' must also be true." ''Modus ponens'' is a mixed hypothetical syllogism and is closely related to another valid form of argument, '' modus tollens''. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of ''modus ponens''. The history of ''modus ponens'' goes back to antiquity. The first to explicitly describe the argument form ''modus ponens'' was Theophrastus. It, along with '' modus tollens'', is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal. Explanation The form of a ''modus ponens'' argument is a mixed hypothetical syllogism, with two premises and a con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitution (logic)
A substitution is a syntactic transformation on formal expressions. To ''apply'' a substitution to an expression means to consistently replace its variable, or placeholder, symbols with other expressions. The resulting expression is called a ''substitution instance'', or ''instance'' for short, of the original expression. Propositional logic Definition Where ''ψ'' and ''φ'' represent formulas of propositional logic, ''ψ'' is a ''substitution instance'' of ''φ'' if and only if ''ψ'' may be obtained from ''φ'' by substituting formulas for propositional variables in ''φ'', replacing each occurrence of the same variable by an occurrence of the same formula. For example: ::''ψ:'' (R → S) & (T → S) is a substitution instance of ::''φ:'' P & Q That is, ''ψ'' can be obtained by replacing P and Q in ''φ'' with (R → S) and (T → S) respectively. Similarly: ::''ψ:'' (A ↔ A) ↔ (A ↔ A) is a substitution instance of: ::''φ:'' (A ↔ A) since ''ψ'' can be obta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formal system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tautology (logic)
In mathematical logic, a tautology (from ) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of what a ball is and regardless of its colour. Tautology is usually, though not always, used to refer to valid formulas of propositional logic. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement. In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be logically c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Depression (mood)
Depression is a mental state of low Mood (psychology), mood and aversion to activity. It affects about 3.5% of the global population, or about 280 million people worldwide, as of 2020. Depression affects a person's thoughts, behavior, feelings, and subjective well-being, sense of well-being. The pleasure or joy that a person gets from certain experiences is reduced, and the afflicted person often experiences a loss of motivation or interest in those activities. People with depression may experience sadness, feelings of dejection or hopelessness, difficulty in thinking and concentration, or a significant change in appetite or time spent sleeping; Suicidal ideation, suicidal thoughts can also be experienced. Depression can have multiple, sometimes overlapping, origins. Depression can be a symptom of some mood disorders, some of which are also commonly called ''depression'', such as major depressive disorder, bipolar disorder and dysthymia. Additionally, depression can be a norm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electroconvulsive Therapy
Electroconvulsive therapy (ECT) is a psychiatry, psychiatric treatment that causes a generalized seizure by passing electrical current through the brain. ECT is often used as an intervention for mental disorders when other treatments are inadequate. Conditions responsive to ECT include major depressive disorder, mania, and catatonia.FDAFDA Executive Summary Prepared for the January 27–28, 2011 meeting of the Neurological Devices Panel Meeting to Discuss the Classification of Electroconvulsive Therapy Devices (ECT). Quote, p. 38: "Three major practice guidelines have been published on ECT. These guidelines include: APA Task Force on ECT (2001); Third report of the Royal College of Psychiatrists' Special Committee on ECT (2004); National Institute for Health and Clinical Excellence (NICE 2003; NICE 2009). There is significant agreement between the three sets of recommendations." The general physical risks of ECT are similar to those of brief general anesthesia. Immediately fol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Myocardial Infarction
A myocardial infarction (MI), commonly known as a heart attack, occurs when Ischemia, blood flow decreases or stops in one of the coronary arteries of the heart, causing infarction (tissue death) to the heart muscle. The most common symptom is retrosternal Angina, chest pain or discomfort that classically radiates to the left shoulder, arm, or jaw. The pain may occasionally feel like heartburn. This is the dangerous type of acute coronary syndrome. Other symptoms may include shortness of breath, nausea, presyncope, feeling faint, a diaphoresis, cold sweat, Fatigue, feeling tired, and decreased level of consciousness. About 30% of people have atypical symptoms. Women more often present without chest pain and instead have neck pain, arm pain or feel tired. Among those over 75 years old, about 5% have had an MI with little or no history of symptoms. An MI may cause heart failure, an Cardiac arrhythmia, irregular heartbeat, cardiogenic shock or cardiac arrest. Most MIs occur d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of Postgraduate education, graduate study and original research. The name of the degree is most often abbreviated PhD (or, at times, as Ph.D. in North American English, North America), pronounced as three separate letters ( ). The University of Oxford uses the alternative abbreviation "DPhil". PhDs are awarded for programs across the whole breadth of academic fields. Since it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and, in some cases, defend their work before a panel of other experts in the field. In many fields, the completion of a PhD is typically required for employment as a university professor, researcher, or scientist. Definition In the context o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Townsend Harris High School
Townsend Harris High School (THHS; often also shortened to Townsend Harris or simply Townsend) is a public high school for the humanities in the New York City borough of Queens. It is located on the campus of Queens College, a public college part of the City University of New York system. The school was named in honor of Townsend Harris, the 19th-century merchant, politician, and diplomat who served as the first American Consul to Japan. The school's students and alumni often refer to themselves as "Harrisites". History Townsend Harris High School was founded in 1984 by alumni of Townsend Harris Hall Prep School, who desired to reopen their school that was closed in the 1940s. This process started in 1980. The first principal was Malcolm Largmann, a former high school English teacher with a strong belief in a classical education who also handpicked the school's original faculty. Largmann served as principal of Townsend Harris from 1984 until his retirement in 2001. He would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
