the beauty of mathematics in computer science pdf

/BBox [0 0 362.835 272.126] /FormType 1 The Viterbi algorithm is the most common algorithm in modern digital communications. Mathematics for Computer Science. 0000014263 00000 n /Filter /FlateDecode STAN-CS-80-786. The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. Andrew Viterbi and Irwin Jacobs co-founded Qualcomm, a leading company of semiconductor and telecommunications in the world that dominated CDMA-based 3G mobile communication standards. %PDF-1.2 %�� /BBox [0 0 362.835 3.985] x��P(�� It is not an exaggeration to say that Andrew Viterbi is one of the scientists whose work has had the most influence on our lives today. endobj 0000000931 00000 n 0000018777 00000 n %PDF-1.5 1.12.4 Using Discrete Mathematics in Computer Science 87 CHAPTER 2 Formal Logic 89 2.1 Introduction to Propositional Logic 89 2.1.1 Formulas 92 2.1.2 Expression Trees for Formulas 94 2.1.3 Abbreviated Notation for Formulas 97 2.1.4 Using Gates to Represent Formulas 98 2.2 Exercises 99 2.3 Truth and Logical Truth 102 Speaking of Andrew Viterbi, perhaps few people outside the communication industry know about him. 95 0 obj Eric Lehman. /Subtype /Form << 0000002391 00000 n Proof. %�� Google Inc. F Thomson Leighton. ��(,�x�o�;Vw��GM0L��fD޻�V]_�ä�i �t\ǔ`��O��u>��lk��~x�AQF��!8rA�6e��yl��1��|6�/�Y�H�Я{?�³�W�U9�eq�< g��>䋢�ƙJ�w�Ib�� stream 0000013104 00000 n Nonetheless, most people in computer science and telecommunications know about the Viterbi algorithm named after him. 0000007883 00000 n << stream /Length 15 /FormType 1 Department of Electrical Engineering and Computer Science x��]�sܸ��_��*!��.��8�un�rYپJ�w�a,�d��=��u��$A�hF�j��53`�t��h��iڪ��;%mÕ ��\6\R.��Y��i��]M4i81 Today, Qualcomm is still a leader in mobile communication in the 4G and 5G eras. /Subtype /Form 0000001739 00000 n 0000004895 00000 n 0000018755 00000 n /Type /XObject Functions Properties of Functions Composition of Injective Functions Theorem If f : A !B and g : B !C are injective functions then also g f is injective. trailer << /Size 393 /Info 355 0 R /Root 365 0 R /Prev 714032 /ID[<974fb63ab34c94e48b12e02b89c30903><974fb63ab34c94e48b12e02b89c30903>] >> startxref 0 %%EOF 365 0 obj << /Pages 361 0 R /Type /Catalog /DefaultGray 362 0 R /DefaultRGB 363 0 R >> endobj 391 0 obj << /S 473 /Filter /FlateDecode /Length 392 0 R >> stream /Resources 51 0 R << E2(kZĘ�9b HFEm�H�^H�}��=ԟd��&OI�ލ��.9�O�#�u&O��K��. /Length 15 /Matrix [1 0 0 1 0 0] 0000005665 00000 n Nonetheless, most people in computer science and telecommunications know about the Viterbi algorithm named after him. << endstream stream /Type /XObject It is also the decoding algorithm widely used in natural language processing. 0000003499 00000 n ��(r��E��w��N(� @N� /Type /XObject >> >> 0000001031 00000 n endobj �U�/��f�/�9�f��l{y��=��N(L#$��޵. 39 0 obj /Filter /FlateDecode /Subtype /Form x��P(�� endstream x��P(�� stream endstream endobj 0000010334 00000 n endobj Albert R Meyer. !�W5 37 0 obj endobj 364 0 obj << /Linearized 1 /O 366 /H [ 1031 730 ] /L 721442 /E 20623 /N 30 /T 714043 >> endobj xref 364 29 0000000016 00000 n stream �r��}dP�I�S��>j�im�\S|D-B!��*�E��Pe5� ǆI�fU;��ч��>1r�|��?��º��M��}�?؎/me9��g�Xb% +�î�c��IXY9��~G -G� 3 �|۷Q+� �k� �tk�tXa��iiԜ�0 ؋+�U®�� 2�M��E��|$��e筰�� B8. /Type /XObject /Length 15 /Subtype /Form /BBox [0 0 362.835 5.313] ]�J8C��?S��KW��K*��q-o ��s/�҃K�T> $�6�ш�hx;r��v��ގc��єZ޾6��Y��b��V]\x��/��0�0BnE�iD�/��_O��d��y_'�s��(7��&kԟ�3T��>,,��΃�}��m�/-��B��I��(��{J=.�� z�V��,sZː��U�x_�!�˲6�Em�W�&B)��GT}]�&7�!׳�Z�g�#I;��X )s�p"A�(g�(,�� /Resources 38 0 R 50 0 obj 0000010311 00000 n << endobj /FormType 1 << /Filter /FlateDecode Simply put, a proof is a method of establishing truth. /Matrix [1 0 0 1 0 0] /Matrix [1 0 0 1 0 0] >> /Resources 42 0 R /Matrix [1 0 0 1 0 0] /FormType 1 Consider arbitrary elements x;y 2A with x 6=y. Registered in England & Wales No. 0000001761 00000 n Yk�zqb4j��b��2�/�5��@��g��\:,T x��P(�� /Filter /FlateDecode revised Monday 18. th. 0000007860 00000 n DOI link for The Beauty of Mathematics in Computer Science, The Beauty of Mathematics in Computer Science book. /Type /XObject �1ٴ�k��j(�O��>Ukt��F��|̍�BT��vWpb�6�n_e��J ,ŋ��ճWP\A��lz��$�I�J��q��6��{6�2��j|J�5s�(_z��jk~��kR[)I5r׊�*,^9�wAU�"�K��H�ڳ��7��_�b*��d��1�**� >> ʸ�%YM]��Ig� c�0�E ��E\c��P��w:��Wa�ܚ��}�ݥ��H �vY��%Su6��|�ElEC��G�s�A��R��E�;2^S�`�|��\�7{� j��R�o!�o��sp�\�[��YH��k��۹o��[wM�`Q�r��?��~˒I�J/��e%��uW3 0000019572 00000 n stream /FormType 1 >> ëd�u� �A��Ig�^W��T�(��¨�B��4�_��vҢ��iX��h��Z�]�nĶp��m�&�kn�1_��чUm��@��ʖ췒5s�� Speaking of Andrew Viterbi, perhaps few people outside the communication industry know about him. 0000011742 00000 n x��P(�� stream >> 0000012693 00000 n /Length 1930 �b>�� ۠�� ;�ŝ�O֑'m�kȑy�T�[ț��< �ѣvz��nR�U�^o쇧h��F\�#�N�"��V0��u�G�$_N�*%t�t�z�]�W�dI&�g��˫U�w/'y6�d��Nّq�LG(\�:N�9�NO�Ln'D|4BN�f#OF �W�|��Ä<4"K)G�w��㩗%r�S6�Ȉ�2�z@�2>��y6-��;Ri��Q�Sg��p�zAa�4-$SN�M��2_�DB�J��3e|8^f�M�[*H4s��(7C��l��u�^��.w��ҽ~H�dJ 43 0 obj /Filter /FlateDecode /BBox [0 0 362.835 15.94] H�b�� > X � @C2 @ � G� '� *�Z�QYX�V�O�.Q75\�n��4d�R Proofs also play a growing role in computer science; they are used to certify that software and hardware will always behave correctly, some-thing that no amount of testing can do. �t��%;��_�-��(!eܡ9�t��~�Y��(-��k�)�FqI�� U4��R�\�y��{Okޯ�K��Lrg�Jh�ji��ϭ��I��ц''�H�9P*�H��=��p��O�`�HiE��5�&:x��n��ew�8rZ�3i��Ytv�b��PV�&58jc��tr�vc��o�3m��Kԭ�J� {��=��TDAi4��v��'sRR�ۘ��X�� #H%k�'on��ᬷ��R�O��&8�(x�#�'�7��z��"v��&�+RbB�sW�ȉf}�$*��`�jt�i��Y�s endstream 0000002085 00000 n /Matrix [1 0 0 1 0 0] Malte Helmert, Gabriele R oger (University of Basel)Discrete Mathematics in Computer Science October 19, 2020 24 / 34. 0000002107 00000 n /Length 15 41 0 obj

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