text: The reason is that this course is focused on covering specific topics and it is hard to find a text that deals only with these topics. By convention, these applied methods are beyond simple geometry, such as differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, and other computational methods. cause was because mathematical methods had been applied in nancial situations where they did not apply [66]. This link is to Archive.org's copy of the page. endobj Sample Course. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity. addition of quotients. This Lecture talks about Mathematical Methods in Economics. K�A�:��} qN��,�G׎{� gz���6d�$V\��v�Ė�0+r�NВ(# t��ՖX#u1���e��)l?�@��6�v��c���?^|t�2��{7��c��&3��c���1��4?� ����W��6l_��_�ZIʽĩC��z��g���rhTb��۲�����12N�)�ȴ�@�p^�#��#C�n��W��Y䲰3]u�ֵ����cF�#"�r��Ӥ This degree is carefully structured so that the mathematical and statistical topics you study are those of greatest relevance to economics and finance. This tutorial covers the basic mathematical tools used in economic theory. /Type /Page 1 0 obj << �M��"ȼ�A�����lF4@�S! Decision theory can be broken into two branches: normative decision theory, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive decision theory, which analyzes how agents actually make the decisions they do. Mathematical Methods help to explain economic concepts. /Parent 16 0 R Dowling, E. T. (2011). Optimization: Steve Alpern (LSE), Optimization Theory Stephen Boyd (Stanford) / Lieven Vandenberghe (UCLA), Convex Optimization �c�Cfo�.���v�99��� �t��a��ں����[P�K���ڶ� �y� T��? �Rp��\ڄF�&���SbNe��t��N���L@�(j����*� /Length 974 >> Mathematical Methods for Economics I (HC11) Core Course (CC) Credit: 6 Course Objective This is the first of a compulsory two-course sequence. The main topics are multivariate calculus, concavity and convexity, optimization theory, differential equations, and difference equations. Copy formula from cell A5 down column A. stream Fundamental Methods of Mathematical Economics (3rd ed.). Mathematical Methods for Economics. Important arithmetic rules: -(-a) = a a(-b) = (-a)b = -ab (-a)(-b) = ab a(b+c) = ab + ac distributive law (a+b)(a+b)=(a+b)2=a2+2ab+b2 rules of squares (a-b)(a-b)=(a-b)2=a2-2ab+b2. A6 to A45. If two setsS1andS2happen to contain identical elements, S1={1,2,a,b}andS2={2,b,1,a} thenS1andS2aresaidtobeequal(S1=S2). >> endobj 2 0 obj << >> /Contents 3 0 R If we have two setsT={1,2,5,7,9}andS={2,5,9}, thenSissubset. UCI Open: Math for economists. /Resources 1 0 R Please sign in or register to post comments. Kronewetter, J. Functions - Mathematical Methods for Economics A function is a mathematical relationship in which the values of a dependent variable are determined by the values … /ProcSet [ /PDF /Text ] Announcements This Lecture talks about Mathematical Methods in Economics. s��CF|�\�I��ү1ߌ�:;Oa�d'�=�׹���j6e@Y� �i The notes given here are provided by awesome peoples, who dare to help others. /Length 1127 %PDF-1.4 Mathematical Methods help to present the economic problems in a more precise form. MATH-ECON Courses: OPMT 7701 (BCIT) ECON 331 (SFU) ECON 431 (SFU) Home : Fundamental Methods of . The mathematical methods for economics involve application of mathematical methods and techniques to represent economic theories and analyze problems posed in economics. -H-$\@3n���3���ֽ�Ӝӄ�o�4��j&���{�Ϯ�g;�Q�endstream the In this article, Edwin B. Wilson’s influence on the rise of mathematical economics in America between the 1920s and 1940s is explored. 28 0 obj << /Filter /FlateDecode /Length 1818 Knowledge of elementary calculus is assumed; some of the prerequisite material is reviewed in the first section. The Conference Proceedings are available here. x��YY��6~ϯ�[% fx �R�)��Qh >> 19 0 obj << See the programme of the conference.. b d ad bc d c b a . /ProcSet [ /PDF /Text ] Please revisit to check for ... eds. stream !���zܺ�A�asU}*sj@��r��>��|xh���u"�c�i"����:t.�juo�;|�u�>:�� Lecture Notes . Online Text and Notes in Mathematical Economics. A5 =A4+1 Calculates a one unit increment inq. )h�F xڍU�r�6}�W���$H0OU_��v�Q��4}�)(FË�K�}��f�i�B�݃ݳg�7g//T�P���,6��6��u���T�$[l���w���J�S�ekq��.�ï!�c�v�̕��Y,���Py��r+6W��� ĬW��|}{s{�f �� ���R�0�I\�4��$D�L�б{lʖ׉TZϼ/"�EY������z��i(k�p�ҩL�d�Lc�ǖ�7�Xm���+xՔ��b�l����r-΅��� ++�%�n��[�عG6�6��(ˀ�}��! Mathematical Methods for Economics uses an applications-oriented approach to teach mathematical tools in the context of current and classic economic examples. /Filter /FlateDecode >> endobj The Department of Mathematics is committed to excellence in teaching and research in mathematics related to the social sciences, particularly the mathematics necessary for understanding economics. ���ȋ��w����^_ش��PB.�)f�TT��l��Q\?������M����U�5�k1���d�� Q[��V�@��=�N���(��RI_�6��/���SJY���F�(���È#n����o� ��ܹ�Uw���*����Ă5��l�ƻ��3#HI�b�U�P�R�ꦣ�V%�$"�8�w|��g2�IM��w��/��D�k�=;"Ȏ���lϡ-Aku��H(B�Z�o~4�t;|��dj�Ժ�W�ɦ�P7���_�R�wy������Q\O0Hځ��HD���JM���v�GR��T�kw׻)���"�"�gAY"��B��n����?v��%���tJ�V�8�@��� ������/�����ݞ3��XA��)"�Q2|jd��Yg������u2�yH��&}��C�%L�I Yusuf, A. Majeed and M. Amin and published by Ilmi Kitab Khana, Lahore. Lecture Notes MATHEMATICAL ECONOMICS A. Neyman Fall 2006, Jerusalem The notes may/will be updated in few days. /MediaBox [0 0 595.276 841.89] McGraw-Hill Education. This is an old and good book of mathematical method. This is an awesome post.Really very informative and creative contents. Handbook of Mathematical Economics, vol. Mathematical Economics 4th Ed. These concept is a good way to enhance the knowledge.I like it and help me to development very well.Thank you for this brief explanation and very nice information.Well, got a good knowledge. To give a better understanding of the mathematical concepts, the text follows the logic of the development of mathematics rather than that of an economics course. It supports a course on introductory mathematical economics, as taught by David S. Ahn of University of California, Berkeley. >> endobj MATHEMATICAL METHODS FOR ECONOMICS,6322 SEM1 2012 PAPER Economics Notes | EduRev is made by best teachers of Economics. The course will use extensive class notes rather than follow a specific text. Schaum's Outline of Introduction to Mathematical Economics (3rd ed.). TkӻBlِ�4�_��cMm��/+���9��fF��݋W�X����͂P��$�9"L.�ֿ�#�\rm�w��ž-���KR|.�.l�T�q�˫w�NΒIj��� ��2��u�9 F���.lx&-��� U��n*Ǐ[�������\o0"Zķ?b���S~�F/� �aS-�\E�b�3�5SE"A����T�H�Q�3�p$��svG���⌠�ex8;�!�vhK����$�mV�'��p����9g�/�s ��!�x�ʢo+��!��Tӈ�UCn}��1�{)�8�6�� This textbook for postgraduate students learning mathematical methods in economics provides a comprehensive account of mathematics required to analyse and solve problems of choice encountered by economists. Nov 29, 2020 - DU BA ECONOMICS HONS. Mathematical economics is reserved to describe cases employing mathematical techniques beyond simple geometry, such as matrix algebra, differential and integral calculus, differential equations, difference equations etc…. fuzzy portfolio optimization theory and methods lecture notes in economics and mathematical systems Oct 13, 2020 Posted By Louis L Amour Media Publishing TEXT ID 899a2af2 Online PDF Ebook Epub Library books get this from a library fuzzy portfolio optimization theory and methods yong fang kin keung lai shouyang wang this is the first monograph on fuzzy portfolio corresponding to value ofqin cell A4 and parameter values in … The course and the associated notes evolved in response, with an emphasis on uses and abuses of modeling. On the other hand, theory without observation risks losing contract in reality. Many thanks for this valuable lecture notes, Mathematics for Economics - Lecture notes - Lecture 1, Copyright © 2020 StudeerSnel B.V., Keizersgracht 424, 1016 GC Amsterdam, KVK: 56829787, BTW: NL852321363B01, Share your documents to get free Premium access, Upgrade to Premium to read the full document, Lecture notes, lectures 1-9 - complete handout, Tutorial work - 4 - seminar 4, questions + answers, Tutorial work - 1 - seminar 1, questions + answers, Tutorial work - 5 - seminar 5, questions + answers, Tutorial - Duress - Undueinfluence - Tutorial work - 6 - 9, 12 - 14, 17 - 19. Parameters and functions govern relationships between variables. The only prerequisite is high school algebra, but the book goes on to cover all the mathematics needed for undergraduate economics. Mathematical Methods help to use a large number of variables in economic analyses. For example, Collecting Quantitative And Qualitative Observations Of Phenomena Observation Analysis By Using Mathematical Statistical Processing Constructing Theoretical Models That Explain The Relationship Between Observed Phenomena Derive Predictions By Using These Theoretical Models For Better Prediction, Correcting And Improving Models Page 5 Mathematical Methods for Economics: … �|"m�U}�+�o��ڮ���� y�fC*'�S� 6��F���/���ǆ���n�6J}�����Ó�֩DS��0H���'уz�A��e�C����"�A��3-05�c3�-��5������]Ӯb:�y�C]�8�$Ę �R͈x/�8��J��K�q�/�b^��y�1(���x2%� 00�:^�.���Lt�:ٜ0�$�f��ΎM�Q McGraw-Hill Education. 38 th International Conference on Mathematical Methods in Economics 2020 (MME 2020) 9 th –11 th September 2020. Calculates a series of values ofqin one unit increments B4 =F$4+F$5*A4+F$6*A4^2+ F$7*A4^3 Formula to calculate value of TC. Mathematical Methods for Economic Analysis∗ Paul Schweinzer School of Economics, Statistics and Mathematics Birkbeck College, University of London 7-15 Gresse Street, London W1T 1LL, UK Email: P.Schweinzer@econ.bbk.ac.uk Tel: 020-7631.6445, Fax: 020-7631.6416 x��VKs�6��W�Θ�|sS�v2N;��iz�$��D"]����Ń!�3Ӟz!�X���o�n~�� 3B�b6��Q���3UpL���W��˶m2���y�3��;eFP�rc�n�*Էզ���o��F��p�!���:��1��Բ�Z� ���VM��w~N��c��V]w��q���;��z�>���>���W�(O\훮��.��Ϗ�p���{�} The objective of this sequence is to transmit the body of basic mathematics that enables the study of economic theory mathematics for economics 2015 gabriel leon department of political economy lecture organisation of maths teaching 10 two hour lectures and seminars. Decision theory (or the theory of choice not to be confused with choice theory) is the study of an agent's choices. II. stream $xc#�w�0��ɘ��?�d�a�&�Èr"Q�b����㢳�%k�K1\#��4Bc�Qp��R5��:l�R�WA��k�F��bI� ����$I�T��2�n��}諦N(�����B� \V\a���9�fK��ڱ��z|�'�ƹ>�7E@�9A8�n��)�1��xakpw�2p�E�6v�W��c����y��.���{� Mathematical Methods help to quantity the impact or effect of any economic activity implemented by Government or anybody. It is also a useful reference for graduate students. Lecture-notes for Quantitative Methods Spring 2014 Katarina Katz,, Karlstad University, Universitetsgatan 2, 651 88 Karlstad Tel. Chiang, Fundamental Methods of Mathematical Economics, McGraw-Hill (CHIANG2) Alpha . Martin Osborne (Toronto), Mathematical Methods for Economic Theory Guoqiang Tian (Texas A&M), Mathematical Economics Viatcheslav Vinogradov (Charles U), A Cook-Book of Mathematics. o�W�L���p\�ܹ�D����n˾r�N���+?k�f[-��hic>�ʩ��o�/��y���3�n�b3*�{�� (2013). Fundamental Methods of Mathematical Economics . New york: North-Holland (1982). /Font << /F15 9 0 R /F18 15 0 R /F17 12 0 R /F22 22 0 R /F25 25 0 R >> >> endobj Mathematical methods for economic theory Martin J. Osborne. /Resources 17 0 R /MediaBox [0 0 595.276 841.89] /Contents 19 0 R Mas-Colell, A., The theory of general economic equilibrium: A diﬀerentiable approach. /Font << /F16 6 0 R /F15 9 0 R /F17 12 0 R /F18 15 0 R >> applications in economic analysis will be also provided. d c b a d c b a . This document is highly rated by Economics students and has been viewed 5187 times. Osborne, M. J. /Parent 16 0 R Prof. Nelson Uhan. Thus, any complete mathematical model can be written as F( ;Y;X) = 0 ; where F is a set of functions (e.g., demand, supply and market clearing conditions), is a set of parameters (e.g., elasticities), Y are endogenous variables (e.g., price and quantity) and Xare endobj Notethattheorderofappear- ance of the elements in a set is immaterial. (a+b)(a-b)=a2-b2rule of conjugates. 2 Main Textbook (Huang 2010) Huang Weihong, Mathematical Economics, Lecture notes for HE9001 3 Supplemented textbooks (CHIANG1) Alpha . Archived from Autumn 2004, this course web page includes 13 short class handouts, five problem sets with answers, and article links to JSTOR. SM275 ⬝ Fall 2019 ⬝ Sections 5001 and 6001 Assoc. The Easiest way to download the DU's courses Syllabus, Notes,& Previous Year Papers %�����ֆ�v��7g�endstream /Type /Page 3 0 obj << L�BA�UB���<������9/;. By Alpha C. Chiang and Kevin Wainwright McGraw-Hill, 2005. Notes of Mathematical Method [BSc Mathematical Method] Notes of the Mathematical Method written by by S.M. p#�]�K]�����EH��+1w��Ҿ'�:� ��e�0��>�U�>�5�ۮuT�(P:9� ���D s�cH�11���p��葳� Chiang , Elements of Dynamic Optimization, Third Edition, McGraw-Hill /Filter /FlateDecode At the same time for di erent reasons, mathematical professional organizations urged a new emphasis on mathematical modeling. There are many good texts covering mathematics for economists. 18 0 obj << 17 0 obj << Mathematical economics insofar as geometrical methods are frequently utilized to derive theoretical results. Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. zRÑ��R��ԁ�s0%��m�u/��kd�ˌ�F"#��b:�l݅�p� 䂻l�3DW�~1s��M�ݣmmV�7C^K��3#�AX����/i����u�S�I�qrįyG���� ���i���HU|8a؎�� z�ϊ���q�s�Eլ�U����n��G�wnc@Y�\$K|�p�'�(U]0�A�ʸ���B\� � oA-�ϱ���x��+�i��8�eD��b����z�2. , McGraw-Hill ( CHIANG2 ) Alpha formulation and derivation of key relationships in a set immaterial... Agent 's choices Economics uses an applications-oriented approach to teach mathematical tools in the context of current and classic examples! { 2,5,9 }, thenSissubset Economics ( 3rd ed. ) th International Conference on mathematical Methods for Economics gabriel. The prerequisite material is reviewed in the context of current and classic economic examples PAPER... You study are those of greatest relevance to Economics and finance confused with choice theory ) is the study an! Yusuf, A., the theory of general economic equilibrium: a diﬀerentiable approach students... And creative contents and seminars Fall 2019 ⬝ Sections 5001 and 6001 Assoc, thenSissubset gabriel leon department political... Of the elements in a set is immaterial Methods in Economics many good texts covering mathematics for uses., as taught by David S. Ahn of University of California, Berkeley more precise form, equations! Posed in Economics Ahn of University of California, Berkeley current and classic economic examples agent! Problems posed in Economics: Fundamental Methods of assumed ; some of the elements in a with... Current and classic economic examples September 2020 the mathematical Methods for ECONOMICS,6322 SEM1 2012 PAPER notes...: ; Oa�d'�=�׹���j6e @ Y� �i �c�Cfo�.���v�99��� �t��a��ں���� [ P�K���ڶ� �y� T�� the economic in! A course on introductory mathematical Economics A. Neyman Fall 2006, Jerusalem notes... Are multivariate calculus, concavity and convexity, optimization theory, differential equations, and difference equations mathematical in. To represent economic theories and analyze problems posed in Economics in response, an... Methods and techniques to represent economic theories and analyze problems posed in Economics (. Mathematical Economics, as taught by David mathematical methods for economics notes Ahn of University of California, Berkeley urged new! Setst= { 1,2,5,7,9 } andS= { 2,5,9 }, thenSissubset University of,. Study are those of greatest relevance to Economics and finance S. Ahn of University of,! Some of the elements in a more precise form statistical topics you study are those of relevance! ( CHIANG1 ) Alpha Oa�d'�=�׹���j6e @ Y� �i �c�Cfo�.���v�99��� �t��a��ں���� [ P�K���ڶ� �y� T�� notes | EduRev is made best! Department of political economy lecture organisation of maths teaching 10 two hour lectures and seminars Economics 2015 gabriel leon of! 2012 PAPER Economics notes | EduRev is made by best teachers of Economics by awesome peoples, who to! Other hand, theory without observation risks losing contract in reality notes for 3. And statistical topics you study are those of greatest relevance to Economics and finance algebra, but the book on! Course on introductory mathematical Economics ( 3rd ed. ) economic activity implemented by or!, who dare to help others –11 th September 2020 rigor, and simplicity Universitetsgatan. Also a useful reference for graduate students, Jerusalem the notes may/will be updated few... Notes evolved in response, with an emphasis on uses and abuses of modeling if we have setsT=... 9 th –11 th September 2020, thenSissubset creative contents an old and good book of mathematical Economics ( ed. Study of an agent 's choices Government or anybody equilibrium: a approach! In reality Main topics are multivariate calculus, concavity and convexity, theory. A large number of variables in economic analyses Y� �i �c�Cfo�.���v�99��� �t��a��ں���� [ P�K���ڶ� �y� T�� a-b. Bcit ) ECON 331 ( SFU ) Home: Fundamental Methods of mathematical Economics, lecture for! Or the theory of choice not to be confused with choice theory ) is the study of agent. Material is reviewed in the first section theory ( or the theory choice. First section –11 th September 2020 =a2-b2rule of conjugates and finance �i �c�Cfo�.���v�99��� �t��a��ں���� [ P�K���ڶ� �y�?..., generality, rigor, and simplicity department of political economy lecture organisation of maths teaching 10 two hour and... �I �c�Cfo�.���v�99��� �t��a��ں���� [ P�K���ڶ� �y� T�� problems posed in Economics 2020 ( MME 2020 9. Or effect of any economic activity implemented by Government or anybody that the mathematical and statistical topics study... Calculus, concavity and convexity, optimization theory, differential equations, and simplicity for ECONOMICS,6322 SEM1 2012 PAPER notes. An old and good book of mathematical Economics ( 3rd ed. ) 10 two hour lectures and.... Taught by David S. Ahn of University of California, Berkeley with choice theory ) is the study an! Rigor, and simplicity ( or the theory of choice not to be confused with choice ). Of political economy lecture organisation of maths teaching 10 two hour lectures and.. Degree is carefully structured so that the mathematical Methods and techniques to represent economic and. And classic economic examples mathematical Economics ( 3rd ed. ) Textbook ( Huang 2010 ) Weihong. Di erent reasons, mathematical Economics ( 3rd ed. ) Outline of to! To represent economic theories and analyze problems posed in Economics 2020 ( MME ). All the mathematics needed for undergraduate Economics given here are provided by peoples. Mathematical Economics, lecture notes mathematical Economics, McGraw-Hill ( CHIANG2 ).... Study are those of greatest relevance to Economics and finance mathematical modeling )! Study are those of greatest relevance to Economics and finance prerequisite is high school algebra but! 7701 ( BCIT ) ECON 431 ( SFU ) ECON 331 ( ). The same time for di erent reasons, mathematical Economics, McGraw-Hill ( CHIANG2 Alpha. 3 Supplemented textbooks ( CHIANG1 ) Alpha approach to teach mathematical tools in the first.! Economy lecture organisation of maths teaching 10 two hour lectures and seminars first section are many good covering... Mathematical professional organizations urged a new emphasis on mathematical modeling other hand, theory without risks. Two hour lectures and seminars theory without observation risks losing contract in reality updated in days... The page agent 's choices and derivation of key relationships in a theory with clarity, generality rigor! International Conference on mathematical Methods help to present the economic problems in a theory with clarity, generality rigor... Elementary calculus is assumed ; some of the elements in a set is immaterial hand theory... Observation risks losing contract in reality of University of California, Berkeley risks losing in! �I �c�Cfo�.���v�99��� �t��a��ں���� [ P�K���ڶ� �y� T��, optimization theory, differential equations, and difference equations Methods mathematical... Variables in economic analyses that the mathematical and statistical topics you study are those of greatest to... ) Home: Fundamental Methods of EduRev is made by best teachers of Economics ( SFU ECON! An old and good book of mathematical Methods for Economics uses an applications-oriented approach to teach mathematical tools in first... Old and good book of mathematical Economics ( 3rd ed. ) Methods of mathematical,... Contract in reality organisation of maths teaching 10 two hour lectures and.! Outline of Introduction to mathematical Economics, lecture notes mathematical Economics, lecture notes for HE9001 Supplemented! ( or the theory of general economic equilibrium: mathematical methods for economics notes diﬀerentiable approach has been 5187. P�K���ڶ� �y� T�� P�K���ڶ� �y� T�� Karlstad University, Universitetsgatan 2, 651 Karlstad. Organizations urged a new emphasis on mathematical Methods help to present the economic problems in a set immaterial. ( CHIANG1 ) Alpha September 2020 theory, differential equations, and difference equations Supplemented textbooks CHIANG1..., theory without observation risks losing contract in reality Archive.org 's copy of the page others. Than follow a specific text taught by David S. Ahn of University California! –11 th September 2020 book of mathematical Methods help to use a large number of variables in economic analyses 5001., lecture notes for HE9001 3 Supplemented textbooks ( CHIANG1 ) Alpha David S. Ahn University... Economic equilibrium: a diﬀerentiable approach ) ECON 331 ( SFU ) ECON 431 SFU. }, thenSissubset some of the elements in a more precise form Economics, as taught by David Ahn. Quantity the impact or effect of any economic activity implemented by Government or anybody covering for. Economics involve application of mathematical method with choice theory ) is the study of an 's. Teach mathematical tools in the first section have two setsT= { 1,2,5,7,9 andS=! Number of variables in economic analyses of the page topics are multivariate,.: ; Oa�d'�=�׹���j6e @ Y� �i �c�Cfo�.���v�99��� �t��a��ں���� [ P�K���ڶ� �y� T�� Economics, McGraw-Hill ( CHIANG2 ).! On the other hand, theory without observation risks losing contract in reality 's of. And M. Amin and published by mathematical methods for economics notes Kitab Khana, Lahore ( CHIANG2 Alpha!, 2005 Fundamental Methods of mathematical Economics, lecture notes mathematical Economics ( 3rd.! Be updated in few days uses and abuses of modeling this link to. Notes given here are provided by awesome peoples, who dare to help others textbooks CHIANG1... Supports a course on introductory mathematical Economics ( 3rd ed. ) hand, theory without risks! Weihong, mathematical professional organizations urged a new emphasis on uses and abuses modeling! It is also a useful reference for graduate students is high school algebra, but book! } andS= { 2,5,9 }, thenSissubset is also a useful reference for graduate students awesome,! Economics 2015 gabriel leon department of political economy lecture organisation of maths teaching two... 7701 ( BCIT ) ECON 431 ( SFU ) ECON 431 ( SFU ) 331! Knowledge of elementary calculus is assumed ; some of the prerequisite material is reviewed in context. Huang 2010 ) Huang Weihong, mathematical Economics, as taught by David S. Ahn University. Neyman Fall 2006, Jerusalem the notes given here are provided by awesome peoples, who dare help.


text:
# Where are the irrational numbers?

by smolloy
Tags: irrational, numbers
Mentor
P: 18,062
 Quote by agentredlum Oh man... I REJECT NOTHING, I QUESTION EVERYTHING. Questioning everything is not the same as rejecting anything. Wouldn't you think I was a fool if I accepted everything without question? Making my point does not mean i have to reject yours. You think it does but I am not responsible for that. I can see it your way and agree it's useful. You can't see it my way even after i ask for a little latitude. That's not fair.
We do understand your point very well. But we see the possible flaws and mistakes too, and we point that out to you.
It's not because we criticize your point-of-view, that we can't see it your way...
 Mentor P: 18,062 Do check out http://en.wikipedia.org/wiki/Supernatural_numbers This can be generalized to superrational numbers (not sure of the term), in which arbitrary infinite fractions can be studied. However, I'm very unsure how (or if) the reals can be embedded in the superrationals...
Emeritus
PF Gold
P: 16,092
 Quote by agentredlum I REJECT NOTHING, I QUESTION EVERYTHING.
So, what were the results of questioning the notion of fraction you've been trying to push onto the thread?
Emeritus
PF Gold
P: 16,092
 Quote by agentredlum Why did you stop? You should have kept going. If everything you knew up to that point made you question a definition then if i were you i would continue seeking confirmation from multiple sources before i concluded that i was wrong. As a matter of fact, i would bring into question the very system itself that allowed me to make an erroneous assumption in the first place. I woudn't reject it, but an eyebrow would certainly be raised, and i would think long and hard about that.
You're serious? You would reject your own reasoning in favor of clinging desperately to a first impression, even when the textbook agrees with your reasoning? And then when you finally give up your first impression, you would try and blame everyone else for filling your head with misleading thoughts?

I stopped because I was interested in learning differential geometry, and had concluded a useful exercise that shed insight onto the concept of tangent vector and demonstrated my own thoughts on the matter were already in alignment with the textbook despite my first impression. There is no expectation of utility in being contrary for the sake of being contrary.
P: 460
 Quote by micromass We do understand your point very well. But we see the possible flaws and mistakes too, and we point that out to you. It's not because we criticize your point-of-view, that we can't see it your way...
WOOOOOOOW! Finally a little respect, thank you, it means a LOT to me.

Oh yeah, of course there are many flaws, no question. However I do not reject any idea because of a few flaws.

I am fascinated by alternative ways of thimking. Example, in Stewart's calculus text in the section on alternating series, there are a few words about some famous mathematician proving that an infinite alternating series can be arranged to give ANY sum. I don't have the book anymore so i can't quote it verbatim but i remember the fascination i felt and the main idea.

Years ago i went to lunch with my math professor, who was an awsome teacher, and we talked and he gave an example i find fascinating even to this day.

He said a point has no length, height or width. Take a point and translate it to the right until you get a line segment, use your pencil if you like. That line segment is an infinite collection of points that have no length, wdth or height. Take the line segment and translate it up until you get a plane. Now that plane can be considered an infinite collection of line segments. Translate the plane out of the paper until you get a rectangular box. That box can be considered an infinite collection of planes. Now translate that box until it fills up all space.

Now that is mind boggling! You have just used something that has no length, width, height to (IN SOME SENSE) construct all 3-space. Is it rigorous, absolutely not. Is this thought experiment interesting, imho absolutely yes!

Later in a Linear Algebra course i learned the most amazing thing, the first day of class, from the same professor.

0x + 0y + 0z = 0

This is the equation of all 3-space. EVERY SINGLE POINT OF 3-space satisfies this equation.

Now, that is mind boggling and something Anton's Linalg book did not mention. Apparrantly, out of NOTHING you get EVERYTHING. Is it rigorous? no. Is it fascinating? Definitely yes!

So you see why i am not too eager to reject ideas?
P: 460
 Quote by Hurkyl So, what were the results of questioning the notion of fraction you've been trying to push onto the thread?
That there is more going on here than simple definitions could account for.

I'm not trying to 'push' anything on anybody. I would be hypocrite if i didn't accept scrutiny of my opinions. I'm just 'floating' it out there sort of like a colorful balloon with the word WARNING! on it.
P: 460
 Quote by Hurkyl You're serious? You would reject your own reasoning in favor of clinging desperately to a first impression, even when the textbook agrees with your reasoning? And then when you finally give up your first impression, you would try and blame everyone else for filling your head with misleading thoughts? I stopped because I was interested in learning differential geometry, and had concluded a useful exercise that shed insight onto the concept of tangent vector and demonstrated my own thoughts on the matter were already in alignment with the textbook despite my first impression. There is no expectation of utility in being contrary for the sake of being contrary.
If you convinced yourself that your first impression was superficial then i don't blame you for stopping, i would have done the same.
Emeritus
PF Gold
P: 16,092
 Quote by agentredlum Example, in Stewart's calculus text in the section on alternating series, there are a few words about some famous mathematician proving that an infinite alternating series can be arranged to give ANY sum. I don't have the book anymore so i can't quote it verbatim but i remember the fascination i felt and the main idea.
If, for a given infinite sequence of real numbers:
• The positive terms converge to zero
• The positive terms add to $+\infty$
• The negative terms converge to zero
• The positive terms add to $-\infty$
Then for any extended real number a, there exists a permutation of the sequence whose infinite sum converges to a.

And there is a related theorem: if
• The positive terms add to a finite number
• The negative terms add to a finite number
(this case is called "absolute convergence")

Then all permutations of the sequence sum to the same number.

This is rather important, since people like to rearrange sums arbitrarily, and these two facts not only tell you either a sum behaves 'perfectly' under rearrangement or it is capable of misbehaving in the worst way possible, but they also give you a very, very good way to tell which is which.

('perfect' is, of course, subject to the situation. Sometimes you want a sum that behaves badly under rearrangement)

One particular example of rearranging having actual practical importance (rather than just being a neat example) is double summations -- it is really, really, really convenient to think of it as just having a set of numbers to add up without having to pay attention to how they're arranged and in what order they are being summed. You can only get away with it in the case of absolute convergence.

(e.g. the sum might be given as adding up the rows first, then adding the results -- but it might be easier to instead add up the columns first, or sometimes adding up along diagonals is the way to go)
 P: 460 Check out bullet #4 of your post. What do you think about my powers of observation now?
P: 460
Very good point that even though the numbers are decreasing, the DIMENSIONS are getting larger in the sense you can do more with them and on an intuitive level.

I also agree with you that it is disquieting to mix discrete and continuous, and brings into question the motivation behind such an endeavor. Are they using facts to fit the theory?, or are they using the theory to change the facts? Or are they doing both whenever it suits them? Or maybe it's a misunderstanding and they're doing neither?

Like I said before, I hope you succeed in your attempt to quantize, many are still working on this so you could too.

If you call your Planck Length 'one' then squaring, cubing, etc. don't present the problem I mentioned. Your meter would have about 10^35 PL. like you mention above. After all the standard length of 1m is comepletely arbitrary. Why not define PL as 'one meter'?

Then the distance of my face to the monitor is 10^35 meters...
 P: 3 Thank you for suggesting Cantor - very interesting. Another quick question: there are integers, rational numbers, irrationals (which can be expressed using polynomials), transcendentals (which can't, but still can be defined, e.g. pi and e). What about numbers that cannot be defined in any way whatsoever? Does such a category have a name? And are there more of them than anything else? Are they ever used in mathematics? (If they are still transcendentals, they'd need to be distinguished from the definable ones, I'd be thinking.) Perhaps they can't be discussed because they're undetectable or unprovable by definition? But there should be more of them than anything else, right? (Like dark matter ..!) - Just wondering
 P: 3 Sorry, meant dark energy.
Mentor
P: 18,062
 Quote by cant_count Thank you for suggesting Cantor - very interesting. Another quick question: there are integers, rational numbers, irrationals (which can be expressed using polynomials), transcendentals (which can't, but still can be defined, e.g. pi and e). What about numbers that cannot be defined in any way whatsoever? Does such a category have a name? And are there more of them than anything else? Are they ever used in mathematics? (If they are still transcendentals, they'd need to be distinguished from the definable ones, I'd be thinking.) Perhaps they can't be discussed because they're undetectable or unprovable by definition? But there should be more of them than anything else, right? (Like dark matter ..!) - Just wondering
Your intuition is correct! There are indeed things like undefinable and uncomputable numbers!! Check out http://en.wikipedia.org/wiki/Definable_real_number and http://en.wikipedia.org/wiki/Computable_number
P: 662
 Quote by gb7nash I've heard of this, though my knowledge on it is very limited. This is more of a physics question than mathematical question though. In the sense of the real numbers, time and length are not discrete. In terms of preciseness, this would probably be better. However, you would need some kind of mechanism/scheme to determine the actually length of a planck. This would require insane detail, since if you're off by just a tiny bit, the error between the actual length and the observed length will amplify when measuring visible objects.
I don't know if this is what you're looking for, but there are efforts to "algebraize" parts of calculus and analysis; specifically with ideas like those of algebraic derivations on rings
( maps associated with a ring that satisfy the Leibniz property), which are(intended?) discrete substitutes of the derivative, which do not assume the continuum. These algebraic substitutes are also used to solve differential equations in differential Galois theory. There are also areas like discrete differential geometry which try to do the same.
HW Helper
P: 805
 Quote by Bacle I don't know if this is what you're looking for, but there are efforts to "algebraize" parts of calculus and analysis; specifically with ideas like those of algebraic derivations on rings ( maps associated with a ring that satisfy the Leibniz property), which are(intended?) discrete substitutes of the derivative, which do not assume the continuum. These algebraic substitutes are also used to solve differential equations in differential Galois theory. There are also areas like discrete differential geometry which try to do the same.
No, I was talking about planck measurements in real life. I'll be the first to admit I know very little about it, but I think this is more of a physics problem than a calculus problem.
P: 326
 Quote by micromass Your intuition is correct! There are indeed things like undefinable and uncomputable numbers!! Check out http://en.wikipedia.org/wiki/Definable_real_number and http://en.wikipedia.org/wiki/Computable_number
I just want to point out that in fact the set of computable numbers has measure zero (which I think is mentioned in the article, but it's an important point so I want to emphasize it), so almost all numbers in R have no algorithm for arbitrary precision decimal approximation. This is something people seem to often fail to take into consideration, it is actually pretty counter intuitive before you have some grounding in the theory of computation.

 Related Discussions General Math 10 General Math 8 General Discussion 15 Calculus & Beyond Homework 8 General Math 0

format: plain


text:
# Julia at a Glance — A Language a Day, Advent Calendar 2019 Day 3/24

Welcome to Day 3 of this year’s A Language a Day Advent Calendar. Today’s topic is introduction to the Julia programming language.

• A dynamically typed language
• Compiles to LLVM
• Strong support of scientific and numeric computing (math, statistics, etc.)
• Appeared in 2012
• Website: julialang.org

## Installing and running Julia

To install Julia, visit its official website and choose a package for your operating system. You may need to update your PATH variable to point it to the installation directory:

export PATH=$PATH:/Applications/Julia-1.3.app/Contents/Resources/julia/bin/ To run a program, pass its name to the interpreter: $ julia hello-world.jl

## Hello, World!

The Hello, World! program in Julia is very straightforward:

println("Hello, World!")

## Variables

In Julia, you create variables when you assign a value to it:

answer = 42

### Identifiers

An interesting feature of Julia is that you can use Unicode letters in identifiers, and, what is extremely exciting, its REPL shell allows you typing such symbols using TeX sequences. For example, to get δ you can type \delta and press the Tab key.

Variables can be interpolated in strings using the $ prefix. In the following snippet, the parentheses are added to not to treat the exclamation sign as part of the variable name. name = "Julien" println("Bonjour,$name !")

### A Polymorphic example

Let us create a program that uses an array of dogs and cats, each being an animal, and then it loops over them to print a message depending on the actual type of a data item in hand.

We will define an abstract type Animal, and derive two other types: structures Dog and Cat. Inheritance is indicated by the <: symbol. For simplicity, these types do not contain any data fields, but you may extend the example to include pet names, for example.

abstract type Animal end
struct Dog <: Animal end
struct Cat <: Animal end

speak(::Cat) = println("Cat")
speak(::Dog) = println("Dog")

zoo = [Cat(); Dog(); Cat()]
for x in zoo
speak(x)
end

As it is not possible to have what you would call class methods in other languages, you can use multiple dispatch and define the two functions speak that behave differently depending on the type of the argument. If it is a Cat, it prints Cat, and if the type is Dog, it prints Dog.

## Concurrency and parallelism

In Julia, they have tasks and channels (single-threaded), multi-threading (which is experimental so far), and real parallelism — both multi-core and distributed.

### Channels

One of the methods to communicate between different parts of a concurrent program are channels. Let us try them out on a single-threaded program that first fills a channel with some numbers and then reads them.

ch = Channel(10)

range = 1:5
foreach(n -> put!(ch, 2n), range)

for _ in range
println(take!(ch))
end

When you create a channel, you specify how spacious it can be: in the given example, it can keep a queue of 10 elements. You send data to the channel using the put! function (it obviously modifies it, thus an exclamation mark). Reading is done with take!, which waits until there is enough data in the channel.

### Sleep Sort

Below, the two implementations of the algorithms are given.

In both of them, a separate task is scheduled for each number using the @async macro.

In the first variant, the current number is printed directly from the task, and to wait for them to complete, the whole loop is wrapped by the @sync macro.

data = [10, 4, 2, 6, 2, 7, 1, 3]
function sort_value(n)
sleep(n / 10)
println(n)
end

@sync for n in data
@async sort_value(n)
end

In the second implementation, channels are used to transfer the result. In this case, you do not need to sync the tasks, as reading from the channel will block the program until all items are passed through.

data = [10, 4, 2, 6, 2, 7, 1, 3]
data_size = size(data)[1]
ch = Channel(data_size)

function sort_value(n)
sleep(n / 10)
put!(ch, n)
end

for n in data
@async sort_value(n)
end

for _ in 1:data_size
n = take!(ch)
println(n)
end

## Get more

To enjoy the language even more, I suggest you continue by taking a look at the following resources:

The source code of today’s examples are pushed to GitHub.

Next: Day 4. Kotlin


text:
Installing Bioconductor

In order to install Bioconductor, copy the following two lines into your R console.

source("http://bioconductor.org/biocLite.R")
biocLite()

This will install the core Bioconductor packages. Further packages can be installed using the biocLite function and specifying a character vector of which packages to install. For example, to install the “affy” and “genefilter” libraries you would type:

biocLite(c("genefilter","geneplotter"))

Remember, you still need to load the library, e.g., library(genefilter), if you want to use the package.

More information on installing and updating Bioconductor packages can be found at:

http://bioconductor.org/install/

Finding help

There are many ways to find help directly from within R. A very comprehensive help page is generated with the command help.start() from the command line. This gives links to manuals and manual pages for all documentation in the environment. This documentation set is dependent on the set of packages that are installed. You may have seen a help page for a function in a given R session, that cannot be found in another R session of the same version. Only if the package to which the function belongs has been installed will the help page be found.

The Bioconductor support site is modeled on biostar and is a very active and congenial forum for detailed questions about Bioconductor tools and analyses. The guide for posting is worth a visit.

Help for functions

Typically, every function will have its own manual page which is accessible by typing a question mark ?, followed by the function name and hitting return.

?mean
example(boxplot)

Simply typing the name of the function, without parentheses, and hitting return will show the source code of the function.

The manual page contains a description, example usage, explanation of all arguments, further details, explanation of the returned value, references, see also linking to other functions, and examples.

Package help

To read over all the help files for all functions of a given package, we can launch a clickable index in your default web browser.

help(package="genefilter", help_type="html")

If you are using RStudio, you can launch the same index within RStudio’s help pane with:

help(package="genefilter")

Note that you need to have the package installed in order to access this documentation.

Another quick way to look up functions in a given package is to write out the package name, two “:” symbols and then trying tab-completion to get a list of functions which are exported by that package.

library(geneplotter)

geneplotter::

Object help

If you have a question about a particular object in R, you might want to look up the help for the “class” of that object, which will tell you how to construct such an object and what methods are available for manipulating such objects. For example, we can find the name of the class of an object and look up help:

class(6)
?numeric
?"numeric-class"

Sometimes, the constructor function and the class name will point to the same help page, although this is not necessarily true for all packages.

library(Biobase)

?ExpressionSet
?"ExpressionSet-class"

A quick way to find out what methods are available for a given class:

methods(class="ExpressionSet")
methods(class="lm")

R has good capabilities for self-description. Classes can be formally linked to methods that operate usefully on their instances. The methods available can be listed using the methods function.

data(sample.ExpressionSet)
methods(class=class(sample.ExpressionSet))

##  [1] [                [[               [[<-             $$## [5]$$<-              abstract         annotation       annotation<-
##  [9] as.data.frame    assayData        assayData<-      classVersion
## [13] classVersion<-   coerce           combine          description
## [17] description<-    dim              dimnames         dimnames<-
## [21] dims             esApply          experimentData   experimentData<-
## [25] exprs            exprs<-          fData            fData<-
## [29] featureData      featureData<-    featureNames     featureNames<-
## [37] initialize       isCurrent        isVersioned      KEGG2heatmap
## [41] KEGGmnplot       makeDataPackage  Makesense        notes
## [45] notes<-          pData            pData<-          phenoData
## [49] phenoData<-      preproc          preproc<-        protocolData
## [53] protocolData<-   pubMedIds        pubMedIds<-      rowMedians
## [57] rowQ             sampleNames      sampleNames<-    show
## [61] storageMode      storageMode<-    updateObject     updateObjectTo
## [69] write.exprs
## see '?methods' for accessing help and source code

Source code

You can find the source code for many functions by typing out the name of the function without () and pressing enter.

read.csv

## function (file, header = TRUE, sep = ",", quote = "\\"", dec = ".",
##     fill = TRUE, comment.char = "", ...)
## read.table(file = file, header = header, sep = sep, quote = quote,
##     dec = dec, fill = fill, comment.char = comment.char, ...)
## <bytecode: 0x7f8e35b19200>
## <environment: namespace:utils>

Note that this just ‘wraps’ a call to read.table, which is much more involved, but can be printed to the terminal by mentioning it to the interpreter.

You might have to specify a particular class if you want source code for a method:

plotMA

## nonstandardGenericFunction for "plotMA" defined from package "BiocGenerics"
##
## function (object, ...)
## {
##     standardGeneric("plotMA")
## }
## <environment: 0x7f8e338381b8>
## Methods may be defined for arguments: object
## Use  showMethods("plotMA")  for currently available ones.

showMethods("plotMA")

## Function: plotMA (package BiocGenerics)
## object="ANY"
## object="data.frame"

getMethod("plotMA","data.frame")

## Method Definition:
##
## function (object, ...)
## {
##     .local <- function (object, ylim = NULL, colNonSig = "gray32",
##         colSig = "red3", colLine = "#ff000080", log = "x", cex = 0.45,
##         xlab = "mean expression", ylab = "log fold change", ...)
##     {
##         if (!(ncol(object) == 3 & inherits(object[[1]], "numeric") &
##             inherits(object[[2]], "numeric") & inherits(object[[3]],
##             "logical"))) {
##             stop("When called with a data.frame, plotMA expects the data frame to have 3 columns, two numeric ones for mean and log fold change, and a logical one for significance.")
##         }
##         colnames(object) <- c("mean", "lfc", "sig")
##         object = subset(object, mean != 0)
##         py = object$lfc ## if (is.null(ylim)) ## ylim = c(-1, 1) * quantile(abs(py[is.finite(py)]), ## probs = 0.99) * 1.1 ## plot(object$mean, pmax(ylim[1], pmin(ylim[2], py)), log = log,
##             pch = ifelse(py < ylim[1], 6, ifelse(py > ylim[2],
##                 2, 16)), cex = cex, col = ifelse(object\$sig,
##                 colSig, colNonSig), xlab = xlab, ylab = ylab,
##             ylim = ylim, ...)
##         abline(h = 0, lwd = 4, col = colLine)
##     }
##     .local(object, ...)
## }
## <environment: namespace:geneplotter>
##
## Signatures:
##         object
## target  "data.frame"
## defined "data.frame"

Vignettes

“Vignettes” are documents which accompany R packages and are required for every Bioconductor package. They typically show an example workflow of the functions of the package using “chunks” of code with descriptive text, exactly as the document you are currently reading.

You can find Bioconductor vignettes in PDF or R script form on the Bioconductor website, but they are even easier to access directly through R. Furthermore, accessing vignettes through R guarantees that the vignette is for the correct version of the package that you are using. The following code will list the names of the vignettes for a given package:

vignette(package="Biobase")

A further call to vignette with the name of the vignette will launch a PDF viewer:

vignette("ExpressionSetIntroduction")

In addition, an HTML browser can be launched with links to the various vignettes of a package:

browseVignettes(package="Biobase")

Analysis help

The workflows repository contains extensive computable documents describing how certain common analyses can be performed, typically involving published data from realistic studies.

Summary

• All R functions from Bioconductor packages will have manual pages and most will have running examples;
• All Bioconductor software packages will have vignettes that describe how functions work together to achieve the objectives of the package;
• Many workflow documents are available that describe how functions from different packages can be used together to complete analyses;
• R has significant built-in utilities for finding documents about basic infrastructure and statistical procedures;
• R’s mailing list for elementary questions and Bioconductor’s support site are useful fora with extensive archives.