Start Date: 07/05/2020
Course Type: Common Course |
Course Link: https://www.coursera.org/learn/ntumlone-mathematicalfoundations
Machine learning is the study that allows computers to adaptively improve their performance with experience accumulated from the data observed. Our two sister courses teach the most fundamental algorithmic, theoretical and practical tools that any user of machine learning needs to know. This first course of the two would focus more on mathematical tools, and the other course would focus more on algorithmic tools. [機器學習旨在讓電腦能由資料中累積的經驗來自我進步。我們的兩項姊妹課程將介紹各領域中的機器學習使用者都應該知道的基礎演算法、理論及實務工具。本課程將較為著重數學類的工具，而另一課程將較為著重方法類的工具。]
Machine learning is the study that allows computers to adaptively improve their performance with exp
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Foundations of mathematics | The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic. |
Univalent foundations | Univalent foundations are compatible with structuralism, if an appropriate (i.e. categorical) notion of mathematical structure is adopted. |
Mathematical Foundations of Quantum Mechanics | The book Mathematical Foundations of Quantum Mechanics (1932) by John von Neumann is an important early work in the development of quantum theory. |
Heinz Foundations | The Heinz Foundations are several charitable foundations founded by members of the Pittsburgh-based Heinz Foods dynasty. |
The Foundations | Also in the 1970s there would be a collaborative attempt between two former members of the Foundations. Original Foundations trombonist Eric Allandale attempted to work with original Foundations drummer Tim Harris. |
Univalent foundations | Univalent foundations originated from the attempts to create foundations of mathematics based on higher category theory. The closest to the univalent foundations were the ideas that Michael Makkai expressed in his visionary paper known as FOLDS. The main distinction between the univalent foundations and the foundations envisioned by Makkai is the recognition that the "higher dimensional analogs of sets" correspond to infinity groupoids and that categories should be considered as higher-dimensional analogs of partially ordered sets. |
New Foundations | In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of "Principia Mathematica". Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name. Much of this entry discusses NFU, an important variant of NF due to Jensen (1969) and exposited in Holmes (1998). In 1940 and 1951 Quine introduced an extension of NF sometimes called "Mathematical Logic" or "ML", that included classes as well as sets. |
The Foundations | In the mid-1970s, while Clem Curtis and the Foundations were on the road, there was also another Foundations line up that was led by Colin Young who were on the road at the same time, who were playing basically the same material. This eventually led to court action which resulted in Curtis being allowed to bill his group as either the Foundations or Clem Curtis & the Foundations. Young was allowed to bill himself as "The New Foundations", or as "Colin Young & the New Foundations". |
Foundations of mathematics | The systematic search for the foundations of mathematics started at the end of the 19th century and formed a new mathematical discipline called mathematical logic, with strong links to theoretical computer science. |
Francke Foundations | In 1946, the presidium of the province of Saxony annulled the legal entity of the Francke Foundations and integrated these including their entire assets into the Martin Luther University Halle-Wittenberg. The Francke Foundations ceased to exist as self-determined Christian institutions, although the pedagogic tradition was continued through schools and the university's pedagogic institutes on the premises of the foundations. |
Univalent foundations | In foundations of mathematics, univalent foundations is an approach to the foundations of constructive mathematics based on the idea that mathematics studies structures on "univalent types" that correspond, under the projection to set-theoretic mathematics, to homotopy types. Univalent foundations are inspired both by the old Platonic ideas of Hermann Grassmann and Georg Cantor and by the "categorical" mathematics in the style of Alexander Grothendieck. It departs from the use of predicate logic as the underlying formal deduction system, replacing it, at the moment, by a version of the Martin-Löf type theory. The development of the univalent foundations is closely related with the development of homotopy type theory. |
Foundations of mathematics | Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. |
Foundations Forum | Concrete/Foundations presented the Outstanding Contribution to Music Award to Van Halen during the event. |
Lotus Foundations | Support for IBM Lotus Foundations products was withdrawn on September 30, 2014. |
Univalent foundations | A fundamental characteristic of the univalent foundations is that they, when combined with the Martin-Löf type theory, provide a practical system for formalization of modern mathematics. A considerable amount of mathematics has been formalized using this system and modern proof assistants such as Coq and Agda. The first such library called "Foundations" was created by Vladimir Voevodsky in 2010. Now Foundations is a part of a larger development with several authors called UniMath. Foundations also inspired other libraries of formalized mathematics, such as the HoTT Coq library and HoTT Agda library, that developed the univalent ideas in new directions. |
Univalent foundations | The main ideas of the univalent foundations were formulated by Vladimir Voevodsky in 2006/2009. The sole reference for the philosophical connections between the univalent foundations and the earlier ideas are Voevodsky's 2014 Bernays lectures. The name "univalence" is due to Voevodsky. A more detailed discussion of the history of some of the ideas that contribute to the current state of the univalent foundations can be found at the page on homotopy type theory. |
Lotus Foundations | Lotus Foundations was introduced to market as a hardware appliance late in 2008 , and a software-only appliance was also made available. In 2010 Lotus Foundations hardware appliance was discontinued and software-only appliance followed suit in Feb., 2011 (IBM Withdrawal Announcement 910-236 ). In June 2011, however, Lotus Foundations software appliance was reinstated on sale , but IBM doesn't sell it directly anymore, distributing it through selected Business Partners instead. |
Francke Foundations | The Francke Foundations (Franckesche Stiftungen), also known as Glauchasche Anstalten in Halle, were founded in 1695 as a Christian, social and educational work by August Hermann Francke (1663–1727), a Pietist, theologian and university professor in Halle, Germany. Francke Foundations are today a modern educational cosmos closely connected with their history. The Francke Foundations are on the German proposal list as a UNESCO World Heritage Site since 1999. |
Univalent foundations | An important milestone for the univalent foundations was the Bourbaki Seminar talk by Thierry Coquand in June 2014. |
Foundations Forum | As well as a cassette featuring unsigned bands, a 3CD sampler was given out at this Foundations Forum. |