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LEADER 00000cam a2200205   4500 
001    u45174 
003    SIRSI 
008    180326s2014    xxu    f b    001 0 eng u 
020    9780262028134 (hardcover : alk. paper) 
049    JURF 
050 00 Q175.32.M38|bS65 2014 
100 1  Spivak, David I.,|d1978- 
245 10 Category theory for the sciences /|cDavid I. Spivak. 
260    Cambridge, Massachusetts :|bThe MIT Press,|c[2014] 
300    viii, 486 pages :|billustrations  (some color) ;|c24 cm. 
504    Includes bibliographical references (pages 475-478) and 
       index. 
520    Category theory was invented in the 1940s to unify and 
       synthesize different areas in mathematics, and it has 
       proven remarkably successful in enabling powerful 
       communication between disparate fields and subfields 
       within mathematics. This book shows that category theory 
       can be useful outside of mathematics as a rigorous, 
       flexible, and coherent modeling language throughout the 
       sciences. Information is inherently dynamic; the same 
       ideas can be organized and reorganized in countless ways, 
       and the ability to translate between such organizational 
       structures is becoming increasingly important in the 
       sciences. Category theory offers a unifying framework for 
       information modeling that can facilitate the translation 
       of knowledge between disciplines. Written in an engaging 
       and straightforward style, and assuming little background 
       in mathematics, the book is rigorous but accessible to non
       -mathematicians. Using databases as an entry to category 
       theory, it begins with sets and functions, then introduces
       the reader to notions that are fundamental in mathematics:
       monoids, groups, orders, and graphs -- categories in 
       disguise. After explaining the big three concepts of 
       category theory -- categories, functors, and natural 
       transformations -- the book covers other topics, including
       limits, colimits, functor categories, sheaves, monads, and
       operads. The book explains category theory by examples and
       exercises rather than focusing on theorems and proofs. It 
       includes more than 300 exercises, with selected solutions.
       Category Theory for the Sciences is intended to create a 
       bridge between the vast array of mathematical concepts 
       used by mathematicians and the models and frameworks of 
       such scientific disciplines as computation, neuroscience, 
       and physics 
650  0 Science|xMathematical models 
650  0 Categories (Mathematics)