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  2. Discrete mathematics - Wikipedia

    en.wikipedia.org/wiki/Discrete_mathematics

    Discrete mathematics is the study of mathematical structures that can be considered "discrete" ... Rosen, Kenneth H.; Michaels, John G. (2000).

  3. Method of undetermined coefficients - Wikipedia

    en.wikipedia.org/wiki/Method_of_undetermined...

    Consider a linear non-homogeneous ordinary differential equation of the form = + (+) = where () denotes the i-th derivative of , and denotes a function of .. The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met: [2]

  4. Rule of replacement - Wikipedia

    en.wikipedia.org/wiki/Rule_of_replacement

    In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression.A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system.

  5. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    In the following rules, (/) is exactly like except for having the term wherever has the free variable . Universal Generalization (or Universal Introduction) (/) _Restriction 1: is a variable which does not occur in .

  6. Outline of discrete mathematics - Wikipedia

    en.wikipedia.org/.../Outline_of_discrete_mathematics

    Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]

  7. Michael Rosen (mathematician) - Wikipedia

    en.wikipedia.org/wiki/Michael_Rosen_(mathematician)

    Rosen is known for his textbooks, especially for the book with co-author Kenneth Ireland on number theory, which was inspired by ideas of André Weil; [1] this book, A Classical Introduction to Modern Number Theory, gives an introduction to zeta functions of algebraic curves, the Weil conjectures, and the arithmetic of elliptic curves.

  8. Proofs of quadratic reciprocity - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_quadratic...

    Ireland, Kenneth; Rosen, Michael (1990), A Classical Introduction to Modern Number Theory, Graduate Texts in Mathematics, Vol. 84 (2nd ed.), New York: Springer , ISBN 0-387-97329-X Lemmermeyer, Franz (2000), Reciprocity Laws: from Euler to Eisenstein , Springer Monographs in Mathematics, Berlin: Springer , ISBN 3-540-66957-4

  9. Rule of division (combinatorics) - Wikipedia

    en.wikipedia.org/wiki/Rule_of_division...

    In combinatorics, the rule of division is a counting principle. It states that there are n/d ways to do a task if it can be done using a procedure that can be carried out in n ways, and for each way w, exactly d of the n ways correspond to the way w.