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Menyatu dengan umat, menyatu dengan bangsa

pemikiran keislaman keindonesiaan HMI, 1947-1997

The Indonesian Muslim Students Association and politics; Islam and politics in Indonesia, 1947-1997.

The Indonesian Muslim Students Association and politics; Islam and politics in Indonesia, 1947-1997.

Integration of Dose Measurements and Model-based Treatment Planning Algorithms

I also want to acknowledge Wolfgang Tome, Susanta Hui, Tim Botun and Gary
Frank for all their help with this thesis. Finally, I want to thank Mom. Dad, Karen
and Gustavo for their unconditional love and support. Gustavo I really do
appreciate ...

Discrete Mathematics

The long-awaited second edition of Norman Bigg's best-selling Discrete Mathematics includes new chapters on statements and proof, logical framework, natural numbers and the integers, in addition to updated chapters from the previous edition. Carefully structured, coherent and comprehensive, each chapter contains tailored exercises and solutions to selected questions and miscellaneous exercises are presented throughout. This is an invaluable text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory and abstract algebra.Key Features:* Contains nine new introductory chapters, in addition to updated chapters from the previous edition* Contains over 1000 individual exercises and selected solutions* Companion website www.oup.com/mathematics/discretemath contains hints and solutions to all exercisesContents:The Language of Mathematics1. Statements and proofs2. Set notation3. The logical framework4. Natural numbers5. Functions6. How to count 7. Integers8. Divisibility and prime numbers9. Fractions and real numbersTechniques10. Principles of counting11. Subsets and designs12. Partition, classification and distribution13. Modular arithmeticAlgorithms and Graphs14. Algorithms and their efficiency15. Graphs16. Trees, sorting and searching17. Bipartite graphs and matching problems18. Digraphs, networks and flows19. Recursive techniquesAlgebraic Methods20. Groups21. Groups of permutations22. Rings, fields and polynomials23. Finite fields and some applications24. Error-correcting codes25. Generating functions26. Partitions of a positive integer27. Symmetry and counting

The text is designed explicitly for mathematicians and computer scientists seeking a first approach to this important topic.