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Be warned. Referential comprehension includes thinking processes such as drawing conclusions, making generalizations and predicting outcomes. ), This week we complete our brief look at mathematical proofs. 3.
Week 8 In this final week of instruction, we look at the beginnings of the important subject known as Real Analysis, where we closely examine the real number system and develop a rigorous foundation for calculus. R7�x���x:T�-�"�����(\ٯ����SQ��J˨|���:W�����9��{�8�����Z�q�*A`Ƨ��/\�5��.��M1���^�}��G�>���m_M�/���������W���_�~����^s�a��\�ߴ�_]�~p��/�@Kx< ��?-�ϖ��������Ν�A�l�c��"��x�ZJ�|��VK_m\&�V�-j��͗����v��e@�#&fP��d*�0F�u>�̟��C�ٙ In Week 2 we continue our discussion of formalized parts of language for use in mathematics. H�b```"VFA~���1�0p 9 0000021705 00000 n THEN do the Problem Set, after which you can view the Problem Set tutorial. This site uses cookies to offer you a better browsing experience: Tableau Certification Dumps & Practice Test, Tableau Desktop Certified Associate Exam 1, Tableau Desktop Certified Associate Exam 2, Tableau Desktop Certified Associate Exam 3, Tableau Server Certified Associate Exam 1, Tableau Server Certified Associate Exam 2, Tableau Certification Preparation Training, CSM Practice Test 2020 | CSM Exam Questions, ScrumAlliance Certified ScrumMaster Exam 1, ScrumAlliance Certified ScrumMaster Exam 2, ScrumAlliance Certified ScrumMaster Exam 3, Scrum.org Professional Scrum Master I – Exam 1, Scrum.org Professional Scrum Master I – Exam 2, Scrum.org Professional Scrum Master I – Exam 3, 10 Best Free Online Accounting Courses & Classes 2020, NYU In Person Classes for 2020-2021 Academic Year, 10 Best Free Online College Courses with Certificates, IBM AI Engineering Professional Certificate. Taught by: Dr. Keith Devlin, Co-founder and Executive Director. endstream endobj startxref The music comes flrst, the score comes later. 0000001197 00000 n 0000001585 00000 n h�b```�f�Ad`��0p,d6�Ű� ���i}_�j?
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. You may find yourself taking a lot longer. %PDF-1.2 %���� Because the topics become more challenging, starting this week we have just one basic lecture cycle (Lecture -> Assignment -> Tutorial -> Problem Set -> Tutorial) each week. (But only where it counts. 0000003666 00000 n Watch the first lecture and answer the in-lecture quizzes; tackle each of the problems in the associated Assignment sheet; THEN watch the tutorial video for the Assignment sheet. University math majors generally regard Real Analysis as extremely difficult, but most of the problems they encounter in the early days stem from not having made a prior study of language use, as we have here.
This week we complete our analysis of language, putting into place the linguistic apparatus that enabled, mathematicians in the 19th Century to develop a formal mathematical treatment of infinity, thereby finally putting Calculus onto a firm footing, three hundred years after its invention. !O�Gwe��v����6�c��ŏ���M"�x��7�ɛ��i0�i. *?|� l�%�/��~~�`��c�C. It can be very informative to see how you rate your own attempt after looking at the work of others.
58 0 obj << /Linearized 1 /O 60 /H [ 840 378 ] /L 58662 /E 22184 /N 10 /T 57384 >> endobj xref 58 21 0000000016 00000 n After you are done peer reviewing, you may want to evaluate your own solution.
cuốn này là background reading theo course introduction to mathematical thinking của stanford, 1/2 đầu nói khá hay về toán, với một người lần đầu tiên tìm hiểu sâu sâu tí về toán thì thấy nhiều thứ rất thú vị. Test Flight provides an opportunity to experience an important aspect of “being a mathematician”: evaluating real mathematical arguments produced by others. 1/2 sau tập trung vào phân tích ngôn ngữ hơi chán vì mình đã … PART I Background Material 3 ... introduction to mathematical thinking.
0000000767 00000 n
The topic this week is the branch of mathematics known as Number Theory. %PDF-1.5 %���� Your Ultimate source of learning through Best Seller Online Courses. )�")IErR��t�%�)GC�S�nT'#hL�P�L��*�iEfzQ���$�lt&+�M?�L'�3�b�C�A�К��bc)@n�2���"y�xFь.
zT7���ׄ�� >6��^��F3>�2C43ԩU If possible, form or join a study group and discuss everything with them. ��q�D� ���3J�C�d`�@�g^u�����b�Uw�z�颔L�$���V(zG��"C_��=~T�I\�}0�t�.D����̆v�E��`�Ԇ\L� �I��L�ΰ^{��b�:�@瓴:�1X=0_H�p�la�� In this course, however, we consider only some very elementary parts of the subject, using them primarily to illustrate mathematical thinking. ���w�����v�����;h4ҹp>�Y�g,�3�*Fܘ-��uBX^)z##�WF*���J���g��#;��Kd��W�wHM�n�J������>�m�#q.0 h��"9���o���YxŌ����P����X\��Bg$�#1S*'K�U43�)L�@����Z����RqA_��q���d1�$.����8:�'8y����ў���܈�[q��'M�FXE��OD�G������9{��2��M����xln��a�S���ww�#��t�>=���i莫��;�Յv�>�#@�Ni����̭+�?��Z���ʠ�����pfelz��6��� Students are very willing to tackle even ‘drill and practice’ if they Now, 150 years later, the changes in society that were facilitated in part by that more complex mathematics, have made that focal shift important not just for professional mathematicians but for everyone who learns math with a view to using it in the world. It explains what this course is about. Expect to spend a lot longer going through the lectures sufficiently well to understand the material. This week we take our first look at mathematical proofs, the bedrock of modern mathematics. �2cH,��K�8��(-�AK�RU!�è�_]#iS��9�x�-�0�S̋d|Y�����m�^��x�^j��)c�e��_X����|l��oj^c4��%��� Q��>�-���[�D�=�}�Yx֔1��HWXҡh�9cy�|&5 ��ǯ0�v��v��f/���_ ��� endstream endobj 64 0 obj << /Type /FontDescriptor /Ascent 750 /CapHeight 698 /Descent -216 /Flags 262176 /FontBBox [ -124 -250 1000 959 ] /FontName /Frutiger-ExtraBlackCn /ItalicAngle 0 /StemV 180 /XHeight 521 >> endobj 65 0 obj << /Type /Font /Subtype /Type1 /FirstChar 32 /LastChar 181 /Widths [ 259 388 536 520 520 852 722 260 333 333 536 600 260 334 260 296 520 520 520 520 520 520 520 520 520 520 260 260 600 600 600 463 800 667 593 593 685 537 500 685 648 314 407 630 500 870 685 704 574 704 611 556 518 648 630 870 630 610 537 333 296 333 600 500 242 556 592 463 592 556 389 592 574 296 296 556 296 868 574 592 592 592 407 444 407 574 556 833 537 556 444 389 222 389 600 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 520 520 259 259 259 259 259 800 259 259 259 259 259 259 259 600 259 259 259 574 ] /Encoding /WinAnsiEncoding /BaseFont /Frutiger-ExtraBlackCn /FontDescriptor 64 0 R >> endobj 66 0 obj << /Type /FontDescriptor /Ascent 750 /CapHeight 698 /Descent -216 /Flags 262176 /FontBBox [ -112 -250 1000 940 ] /FontName /Frutiger-BoldCn /ItalicAngle 0 /StemV 124 /XHeight 515 >> endobj 67 0 obj << /Type /Font /Subtype /Type1 /FirstChar 32 /LastChar 255 /Widths [ 260 370 519 520 520 833 648 260 296 296 519 600 260 315 260 278 520 520 520 520 520 520 520 520 520 520 260 260 600 600 600 463 800 611 556 556 630 500 463 648 611 278 352 574 444 815 648 648 519 648 556 500 481 611 574 833 574 556 500 296 278 296 600 500 222 500 537 426 537 500 333 537 519 260 260 500 260 778 519 537 537 537 352 407 352 519 481 741 463 463 407 333 222 333 600 260 611 611 556 500 648 648 611 500 500 500 500 500 500 426 500 500 500 500 260 260 260 260 519 537 537 537 537 537 519 519 519 519 520 400 520 520 519 500 600 537 800 800 1000 222 222 260 833 648 260 600 260 260 520 519 260 260 260 260 260 352 352 260 776 537 463 370 600 260 520 260 260 519 519 1000 260 611 611 648 833 815 500 1000 519 519 260 260 600 260 463 556 167 520 296 296 574 574 520 259 260 519 926 611 500 611 500 500 278 278 278 278 648 648 260 648 611 611 611 260 222 222 222 222 222 222 222 222 222 222 ] /Encoding /MacRomanEncoding /BaseFont /Frutiger-BoldCn /FontDescriptor 66 0 R >> endobj 68 0 obj << /Type /ExtGState /SA true /SM 0.02 /TR /Identity >> endobj 69 0 obj << /Type /ExtGState /SA false /SM 0.02 /TR /Identity >> endobj 70 0 obj << /Length 383 /Filter /FlateDecode >> stream AFTER THAT, Lecture 1 prepares the groundwork for the course; then in Lecture 2 we dive into the first topic. You may find yourself taking a lot longer.
2. h�bbd``b`z$��Xe@�m)�`� j5��k|q̹m����ik��@ջd-U��}X��i���"zU�Ұ]�:���dɇ']���^\��8I�T�%&|��������@�ƈ��I��"s%��\�S;�l��4TP��0 0K ���%:�t(� 0000021933 00000 n It is all about being precise and unambiguous. �,1� )�ZXO�+�XǰÐa��"w���L7��3�g�ἠ�0�)�s���) ��Oe endstream endobj 78 0 obj 272 endobj 60 0 obj << /Type /Page /Parent 55 0 R /Resources 61 0 R /Contents 63 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 61 0 obj << /ProcSet [ /PDF /Text /ImageC /ImageI ] /Font << /F5 65 0 R /F6 67 0 R >> /XObject << /Im1 71 0 R >> /ExtGState << /GS1 69 0 R /GS2 68 0 R /GS3 76 0 R >> /ColorSpace << /Cs9 62 0 R >> >> endobj 62 0 obj [ /Indexed /DeviceCMYK 255 70 0 R ] endobj 63 0 obj << /Length 945 /Filter /FlateDecode >> stream
Week 8 In this final week of instruction, we look at the beginnings of the important subject known as Real Analysis, where we closely examine the real number system and develop a rigorous foundation for calculus. R7�x���x:T�-�"�����(\ٯ����SQ��J˨|���:W�����9��{�8�����Z�q�*A`Ƨ��/\�5��.��M1���^�}��G�>���m_M�/���������W���_�~����^s�a��\�ߴ�_]�~p��/�@Kx< ��?-�ϖ��������Ν�A�l�c��"��x�ZJ�|��VK_m\&�V�-j��͗����v��e@�#&fP��d*�0F�u>�̟��C�ٙ In Week 2 we continue our discussion of formalized parts of language for use in mathematics. H�b```"VFA~���1�0p 9 0000021705 00000 n THEN do the Problem Set, after which you can view the Problem Set tutorial. This site uses cookies to offer you a better browsing experience: Tableau Certification Dumps & Practice Test, Tableau Desktop Certified Associate Exam 1, Tableau Desktop Certified Associate Exam 2, Tableau Desktop Certified Associate Exam 3, Tableau Server Certified Associate Exam 1, Tableau Server Certified Associate Exam 2, Tableau Certification Preparation Training, CSM Practice Test 2020 | CSM Exam Questions, ScrumAlliance Certified ScrumMaster Exam 1, ScrumAlliance Certified ScrumMaster Exam 2, ScrumAlliance Certified ScrumMaster Exam 3, Scrum.org Professional Scrum Master I – Exam 1, Scrum.org Professional Scrum Master I – Exam 2, Scrum.org Professional Scrum Master I – Exam 3, 10 Best Free Online Accounting Courses & Classes 2020, NYU In Person Classes for 2020-2021 Academic Year, 10 Best Free Online College Courses with Certificates, IBM AI Engineering Professional Certificate. Taught by: Dr. Keith Devlin, Co-founder and Executive Director. endstream endobj startxref The music comes flrst, the score comes later. 0000001197 00000 n 0000001585 00000 n h�b```�f�Ad`��0p,d6�Ű� ���i}_�j?
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. You may find yourself taking a lot longer. %PDF-1.2 %���� Because the topics become more challenging, starting this week we have just one basic lecture cycle (Lecture -> Assignment -> Tutorial -> Problem Set -> Tutorial) each week. (But only where it counts. 0000003666 00000 n Watch the first lecture and answer the in-lecture quizzes; tackle each of the problems in the associated Assignment sheet; THEN watch the tutorial video for the Assignment sheet. University math majors generally regard Real Analysis as extremely difficult, but most of the problems they encounter in the early days stem from not having made a prior study of language use, as we have here.
This week we complete our analysis of language, putting into place the linguistic apparatus that enabled, mathematicians in the 19th Century to develop a formal mathematical treatment of infinity, thereby finally putting Calculus onto a firm footing, three hundred years after its invention. !O�Gwe��v����6�c��ŏ���M"�x��7�ɛ��i0�i. *?|� l�%�/��~~�`��c�C. It can be very informative to see how you rate your own attempt after looking at the work of others.
58 0 obj << /Linearized 1 /O 60 /H [ 840 378 ] /L 58662 /E 22184 /N 10 /T 57384 >> endobj xref 58 21 0000000016 00000 n After you are done peer reviewing, you may want to evaluate your own solution.
cuốn này là background reading theo course introduction to mathematical thinking của stanford, 1/2 đầu nói khá hay về toán, với một người lần đầu tiên tìm hiểu sâu sâu tí về toán thì thấy nhiều thứ rất thú vị. Test Flight provides an opportunity to experience an important aspect of “being a mathematician”: evaluating real mathematical arguments produced by others. 1/2 sau tập trung vào phân tích ngôn ngữ hơi chán vì mình đã … PART I Background Material 3 ... introduction to mathematical thinking.
0000000767 00000 n
The topic this week is the branch of mathematics known as Number Theory. %PDF-1.5 %���� Your Ultimate source of learning through Best Seller Online Courses. )�")IErR��t�%�)GC�S�nT'#hL�P�L��*�iEfzQ���$�lt&+�M?�L'�3�b�C�A�К��bc)@n�2���"y�xFь.
zT7���ׄ�� >6��^��F3>�2C43ԩU If possible, form or join a study group and discuss everything with them. ��q�D� ���3J�C�d`�@�g^u�����b�Uw�z�颔L�$���V(zG��"C_��=~T�I\�}0�t�.D����̆v�E��`�Ԇ\L� �I��L�ΰ^{��b�:�@瓴:�1X=0_H�p�la�� In this course, however, we consider only some very elementary parts of the subject, using them primarily to illustrate mathematical thinking. ���w�����v�����;h4ҹp>�Y�g,�3�*Fܘ-��uBX^)z##�WF*���J���g��#;��Kd��W�wHM�n�J������>�m�#q.0 h��"9���o���YxŌ����P����X\��Bg$�#1S*'K�U43�)L�@����Z����RqA_��q���d1�$.����8:�'8y����ў���܈�[q��'M�FXE��OD�G������9{��2��M����xln��a�S���ww�#��t�>=���i莫��;�Յv�>�#@�Ni����̭+�?��Z���ʠ�����pfelz��6��� Students are very willing to tackle even ‘drill and practice’ if they Now, 150 years later, the changes in society that were facilitated in part by that more complex mathematics, have made that focal shift important not just for professional mathematicians but for everyone who learns math with a view to using it in the world. It explains what this course is about. Expect to spend a lot longer going through the lectures sufficiently well to understand the material. This week we take our first look at mathematical proofs, the bedrock of modern mathematics. �2cH,��K�8��(-�AK�RU!�è�_]#iS��9�x�-�0�S̋d|Y�����m�^��x�^j��)c�e��_X����|l��oj^c4��%��� Q��>�-���[�D�=�}�Yx֔1��HWXҡh�9cy�|&5 ��ǯ0�v��v��f/���_ ��� endstream endobj 64 0 obj << /Type /FontDescriptor /Ascent 750 /CapHeight 698 /Descent -216 /Flags 262176 /FontBBox [ -124 -250 1000 959 ] /FontName /Frutiger-ExtraBlackCn /ItalicAngle 0 /StemV 180 /XHeight 521 >> endobj 65 0 obj << /Type /Font /Subtype /Type1 /FirstChar 32 /LastChar 181 /Widths [ 259 388 536 520 520 852 722 260 333 333 536 600 260 334 260 296 520 520 520 520 520 520 520 520 520 520 260 260 600 600 600 463 800 667 593 593 685 537 500 685 648 314 407 630 500 870 685 704 574 704 611 556 518 648 630 870 630 610 537 333 296 333 600 500 242 556 592 463 592 556 389 592 574 296 296 556 296 868 574 592 592 592 407 444 407 574 556 833 537 556 444 389 222 389 600 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 259 520 520 259 259 259 259 259 800 259 259 259 259 259 259 259 600 259 259 259 574 ] /Encoding /WinAnsiEncoding /BaseFont /Frutiger-ExtraBlackCn /FontDescriptor 64 0 R >> endobj 66 0 obj << /Type /FontDescriptor /Ascent 750 /CapHeight 698 /Descent -216 /Flags 262176 /FontBBox [ -112 -250 1000 940 ] /FontName /Frutiger-BoldCn /ItalicAngle 0 /StemV 124 /XHeight 515 >> endobj 67 0 obj << /Type /Font /Subtype /Type1 /FirstChar 32 /LastChar 255 /Widths [ 260 370 519 520 520 833 648 260 296 296 519 600 260 315 260 278 520 520 520 520 520 520 520 520 520 520 260 260 600 600 600 463 800 611 556 556 630 500 463 648 611 278 352 574 444 815 648 648 519 648 556 500 481 611 574 833 574 556 500 296 278 296 600 500 222 500 537 426 537 500 333 537 519 260 260 500 260 778 519 537 537 537 352 407 352 519 481 741 463 463 407 333 222 333 600 260 611 611 556 500 648 648 611 500 500 500 500 500 500 426 500 500 500 500 260 260 260 260 519 537 537 537 537 537 519 519 519 519 520 400 520 520 519 500 600 537 800 800 1000 222 222 260 833 648 260 600 260 260 520 519 260 260 260 260 260 352 352 260 776 537 463 370 600 260 520 260 260 519 519 1000 260 611 611 648 833 815 500 1000 519 519 260 260 600 260 463 556 167 520 296 296 574 574 520 259 260 519 926 611 500 611 500 500 278 278 278 278 648 648 260 648 611 611 611 260 222 222 222 222 222 222 222 222 222 222 ] /Encoding /MacRomanEncoding /BaseFont /Frutiger-BoldCn /FontDescriptor 66 0 R >> endobj 68 0 obj << /Type /ExtGState /SA true /SM 0.02 /TR /Identity >> endobj 69 0 obj << /Type /ExtGState /SA false /SM 0.02 /TR /Identity >> endobj 70 0 obj << /Length 383 /Filter /FlateDecode >> stream AFTER THAT, Lecture 1 prepares the groundwork for the course; then in Lecture 2 we dive into the first topic. You may find yourself taking a lot longer.
2. h�bbd``b`z$��Xe@�m)�`� j5��k|q̹m����ik��@ջd-U��}X��i���"zU�Ұ]�:���dɇ']���^\��8I�T�%&|��������@�ƈ��I��"s%��\�S;�l��4TP��0 0K ���%:�t(� 0000021933 00000 n It is all about being precise and unambiguous. �,1� )�ZXO�+�XǰÐa��"w���L7��3�g�ἠ�0�)�s���) ��Oe endstream endobj 78 0 obj 272 endobj 60 0 obj << /Type /Page /Parent 55 0 R /Resources 61 0 R /Contents 63 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 61 0 obj << /ProcSet [ /PDF /Text /ImageC /ImageI ] /Font << /F5 65 0 R /F6 67 0 R >> /XObject << /Im1 71 0 R >> /ExtGState << /GS1 69 0 R /GS2 68 0 R /GS3 76 0 R >> /ColorSpace << /Cs9 62 0 R >> >> endobj 62 0 obj [ /Indexed /DeviceCMYK 255 70 0 R ] endobj 63 0 obj << /Length 945 /Filter /FlateDecode >> stream