Àwọn Ààyè-iṣẹ́ · College

Discrete Mathematics

Logic, proof, induction, relations, counting, recurrences, graphs, automata and complexity: the discrete maths of a first university course.

8 Ìṣàmúlò-ètò 124 Àwọn ìwé-ìwé 150 Àwọn àtòjọ-ètò 180 Àwọn àkóónú àtòjọ-ẹ̀yàn

A complete first university course in discrete mathematics, in the order it is usually taught: propositional and predicate logic and the standard proof techniques; induction in all its forms; sets, relations and functions, including countable and uncountable sets; counting with the product rule, bijections and the pigeonhole principle; recurrence relations and how to solve them; graphs, trees, Euler and Hamilton paths and colouring; Boolean algebra, circuits and finite automata; and finally algorithms, asymptotic analysis, the master theorem, satisfiability and polynomial-time reductions.

It is for anyone comfortable with school algebra who wants to reason precisely about finite and countable structures, and it is the mathematical core of a computer science degree. Each unit ends with a quiz mixing computation, concepts and short proofs; the final exam covers the whole course.

Tí a bá ṣẹ̀dà: Algebra

Àwọn Ìjádè

Logic and proof
25 Àwọn ìwé-ìwé

What is Discrete Mathematics?Discrete Structures Discrete mathematics Truth tables Mathematical Statements Statements and Quantifiers Compound Statements Constructing Truth Tables Truth Tables for the Conditional and Biconditional Implications Equivalent Statements De Morgan’s Laws Rules of Logic Logical Arguments Predicate logic and quantifiers Proofs Direct proof, contrapositive and contradiction Proofs about Discrete Structures Chapter Summary Propositional calculus Logical connective Truth table First-order logic Quantifier (logic)Predicate (mathematical logic)

Fi wọlé láti mú ìṣàmúlò-ètò náà
Induction and sequences
11 Àwọn ìwé-ìwé

Sums and induction Proof by induction Proof by Induction Strong Induction Strong induction and the well-ordering principle Describing Sequences Polynomial Sequences Exponential Sequences Chapter Summary Well-order Peano axioms

Fi wọlé láti mú ìṣàmúlò-ètò náà
Sets, relations and functions
20 Àwọn ìwé-ìwé

Sets Relations: equivalence relations and partial orders Functions Functions and cardinality Introduction to Number Theory Cryptography Cartesian product Power set Binary relation Equivalence relation Partial order Function (mathematics)Injective function Surjective function Bijection Composite function Inverse function Cardinal number Countable set Uncountable set

Fi wọlé láti mú ìṣàmúlò-ètò náà
Counting
16 Àwọn ìwé-ìwé

Counting: rules, choices and bijections The pigeonhole principle Voting Methods Fairness in Voting Methods Standard Divisors, Standard Quotas, and the Apportionment Problem Apportionment Methods Fairness in Apportionment Methods Enumerative combinatorics Permutation Combination Binomial coefficient Pascal's triangle Pigeonhole principle Inclusion–exclusion principle Bijective proof Double counting (proof technique)

Fi wọlé láti mú ìṣàmúlò-ètò náà
Recursion and recurrence relations
7 Àwọn ìwé-ìwé

Recursion Recurrence relation Solving linear recurrence relations Generating Functions Recurrence relation Generating function Catalan number

Fi wọlé láti mú ìṣàmúlò-ètò náà
Graphs and trees
18 Àwọn ìwé-ìwé

Graphs: degrees, paths and connectivity Trees and spanning trees Euler and Hamilton paths Graph colouring Graph theory Graph (discrete mathematics)Degree (graph theory)Path (graph theory)Cycle (graph theory)Connectivity (graph theory)Tree (graph theory)Spanning tree Eulerian path Hamiltonian path Bipartite graph Planar graph Graph coloring Adjacency matrix

Fi wọlé láti mú ìṣàmúlò-ètò náà
Boolean algebra and automata
7 Àwọn ìwé-ìwé

Binary number Boolean algebra Boolean algebra and logic circuits Formal language Automata theory Finite automata and regular languages Turing machine

Fi wọlé láti mú ìṣàmúlò-ètò náà
Algorithms and complexity
15 Àwọn ìwé-ìwé

Algorithms and growth of functions Algorithm Rate of Growth Big O notation Asymptotic analysis, recursion trees and the master theorem Sorting algorithm Computational complexity theory Decision problems, satisfiability and reductions Math and Art Math and the Environment Math and Medicine Math and Music Math and Sports Computability theory Halting problem

Fi wọlé láti mú ìṣàmúlò-ètò náà

Àwọn ìwé-ìwé ìparí

Questions from every unit, the hardest ones last. Typed answers are marked by the algebra system; proofs and photographed working are read by a model; then a person reviews the whole paper before your result is released. Pass and you get a certificate with its own link. Àwọn àmì-ìwé ìṣàmúlò-ètò: 70%.

Fi wọlé

Àwọn ìṣàmúlò-ètò

$39

Àwọn ààyè-iṣẹ́ gbogbo, àwọn ìwé-ìwé ìparí nípa ìṣàfarawé, àti àwọn ìṣàmúlò-ètò 20 tí o ń ṣiṣẹ́, fún ìṣàmúlò-ètò kan.

Rá àwọn àkóónú àwọn ìṣàmúlò-ètò

Àwọn ìwé-ìwé àìpẹ̀

$15

A single sitting of one course's final, marked and reviewed. For someone who already knows the material and wants it tested.

Rá àwọn àwọn àkóónú

Àwọn Ìjánu-ìsún

$19/Àwọn àwọn ààyè-iṣẹ́

Àwọn àwọn ìṣàmúlò-ètò àti àwọn ìṣàmúlò-ètò gbogbo nínú àwọn ìwé-ìwé (ìwé-ìwé meji nínú àwọn ìwé-ìwé kan nínú oṣù) àti àwọn ìṣàmúlò-ètò iṣẹ́ 100 nínú oṣù. Gbàyàn láti inú àwọn

Fi pamọ́

Àwọn ìṣàmúlò-ètò ìṣàmúlò-ètò

Àwọn ìṣàmúlò-ètò mẹ́tà: fi àwòrán tí a tí n ṣiṣẹ́ pamọ́, tàbí tẹ̀ rẹ̀, àti wò ibi tí a tì fi ṣẹ́.

Rá àwọn

Ṣayẹwo àwọn ààyè-iṣẹ́ rẹ̀

Discrete Mathematics

Àwọn Ìjádè

Logic and proof

Induction and sequences

Sets, relations and functions

Counting

Recursion and recurrence relations

Graphs and trees

Boolean algebra and automata

Algorithms and complexity

Àwọn ìwé-ìwé ìparí

Àwọn ìṣàmúlò-ètò

Àwọn ìṣàmúlò-ètò

Àwọn ìwé-ìwé àìpẹ̀

Àwọn Ìjánu-ìsún

Àwọn ìṣàmúlò-ètò ìṣàmúlò-ètò