
Overview
Overview
وصف المقرر:
في مقرر CS285: Discrete Math for Computing، راح نتعلم الـ fundamentals اللي تشكل العمود الفقري لعلوم الـ Computer Science.
المقرر يغطي مواضيع متنوعة تساعدك تطور مهارات مهمة مثل الـ logical thinking و الـmathematical analysis، منها:
- Foundation of Logic: لفهم كيفية صياغة وتحليل العبارات المنطقية.
- Sets, Functions, and Sequences: لتعزيز فهمك لبنية البيانات وتنظيمها.
- Number Theory and Cryptography: لفهم التطبيقات الأمنية وكيفية حماية البيانات.
- Induction and Recursion: لتطوير طرق برمجية لحل المشكلات المتكررة.
- Counting and Its Techniques: لفهم طرق حساب التركيبات والاحتمالات.
- Graphs and Relations: لتحليل العلاقات بين البيانات وحل المشكلات العملية.
ماذا ستحصل عند الاشتراك في هذا المقرر؟
- فيديوهات تعليمية قصيرة: تغطي جميع المواضيع بتسلسل واضح وسلس.
- تمارين عملية: تشمل تطبيقات على مفاهيم العد، الرسوم البيانية، والعلاقات.
- مجموعة whatsapp خاصة: للرد على استفساراتك ومساعدتك على فهم المادة بشكل أعمق مع زملائك الطموحين.
- مراجعات شاملة للاختبارات: تضمن استعدادك الكامل للامتحانات النهائية.
ملاحظات هامة:
- الاشتراك في المقرر لمدة ترم واحد فقط
- الاشتراك لا يشمل بثوث مباشرة.
- لا يتم حل الواجبات أو المشاريع نيابة عنك.
هذا المقرر ليس مجرد مادة دراسية، بل هو مفتاح لفهم أساسيات الحوسبة وتطبيق الرياضيات المتقطعة في حل مشكلات الحياة الواقعية.
Course Features
- Lectures 215
- Quiz 0
- Duration 22 weeks
- Skill level All levels
- Language Arabic
- Students 49
- Assessments Yes
Curriculum
Curriculum
Curriculum
- 22 Sections
- 215 Lessons
- 22 Weeks
Expand all sectionsCollapse all sections
- Introduction2
- Foundation of Logic22
- 2.1Propositions20 Minutes
- 2.2Converse, Inverse, & Counterpositive4 Minutes
- 2.3Translating English to Propositions5 Minutes
- 2.4Biconditional5 Minutes
- 2.5Exercise on truth table7 Minutes
- 2.6Logical Equivalence Laws15 Minutes
- 2.7Exercises on Logical Equivalence5 Minutes
- 2.8Consistency5 Minutes
- 2.9DNF & CNF3 Minutes
- 2.10Quantifiers10 Minutes
- 2.11Negating Quantifiers9 Minutes
- 2.12Nested Quantifiers9 Minutes
- 2.13Exercise on Nested Quantifiers
- 2.14Predicate Logic7 Minutes
- 2.15Rules of Inference11 Minutes
- 2.16Quantified Rules of Inference9 Minutes
- 2.17Proofs (Not included this semester)
- 2.18Direct Proof (Not included this semester)
- 2.19Indirect Proof (Not included this semester)
- 2.20Exercise on Indirect Proof (Not included this semester)
- 2.21Proof by Contradiction (Not included this semester)
- 2.22Proof by Cases (Not included this semester)
- Revision for Foundations of Logic6
- Sets, Functions, and Sequences30
- 4.1Sets4 Minutes
- 4.2Sets(2)4 Minutes
- 4.3Set Equality and Subsets9 Minutes
- 4.4Set Cardinality and Power Sets8 Minutes
- 4.5Exercise on cardinality3 Minutes
- 4.6Set Operations8 Minutes
- 4.7Exercise on Set Operations7 Minutes
- 4.8Set Identities8 Minutes
- 4.9Proving Set Identities8 Minutes
- 4.10Extended Set Operations14 Minutes
- 4.11Functions7 Minutes
- 4.12Functions(2)
- 4.13Exercise on Functions6 Minutes
- 4.14Inverse Functions4 Minutes
- 4.15Composition of Functions2 Minutes
- 4.16Sequences7 Minutes
- 4.17Geometric Sequence3 Minutes
- 4.18Guessing Sequence
- 4.19Exercise on Guessing Sequences6 Minutes
- 4.20Summation7 Minutes
- 4.21Summation of Arithmetic Sequence4 Minutes
- 4.22Summation of Geometric Sequence5 Minutes
- 4.23Recurrence Relations3 Minutes
- 4.24Recurrence Relations (2)4 Minutes
- 4.25Exercise on Recurrence Relations4 Minutes
- 4.26Matrices3 Minutes
- 4.27Adding Matrices1 Minute
- 4.28Multiplying Matrices5 Minutes
- 4.29Matrix Conjunction & Disjunction2 Minutes
- 4.30Properties of Matrices12 Minutes
- Revision for Sets, Functions, & Sequences8
- Major I11
- Number Theory and Cryptography29
- 7.1Division4 Minutes
- 7.2Division Algorithm2 Minutes
- 7.3Modular Arithmetic3 Minutes
- 7.4Modular Arithmetic (2)4 Minutes
- 7.5Prime Numbers3 Minutes
- 7.6Trial Division7 Minutes
- 7.7Greatest Common Divisor7 Minutes
- 7.8Dividing Congruences6 Minutes
- 7.9Least Common Multiple4 Minutes
- 7.10Division Algorithm (2) (Not included this semester)4 Minutes
- 7.11Euclidean Algorithm (Not included this semester)8 Minutes
- 7.12Linear Combination (Not included this semester)12 Minutes
- 7.13Linear Combination (2) (Not included this semester)13 Minutes
- 7.14Inverse of Linear Congruence7 Minutes
- 7.15Inverse Using Euclidean Algorithm (Not included this semester)18 Minutes
- 7.16Solving Congruences Using Inverse (Not included this semester)4 Minutes
- 7.17Chinese Theorem (Not included this semester)19 Minutes
- 7.18Exercise on Chinese Theorem (Not included this semester)18 Minutes
- 7.19Fermat’s Theorem (Not included this semester)9 Minutes
- 7.20Euler’s Totient Function (Not included this semester)9 Minutes
- 7.21Euler’s Generalization (Not included this semester)7 Minutes
- 7.22UPCs (Not included this semester)5 Minutes
- 7.23ISBN (Not included this semester)10 Minutes
- 7.24Shift Cipher12 Minutes
- 7.25Aphine Cypher14 Minutes
- 7.26RSA Cryptosystem14 Minutes
- 7.27Note on RSA2 Minutes
- 7.28Diffie-Hellman Protocol7 Minutes
- 7.29Digital Signatures
- Revision for Nymber Theory & Cryptography2
- Induction and Recursion7
- Revision for Induction & Recursion2
- Counting13
- 11.1Intro to Counting4 Minutes
- 11.2Product Rule11 Minutes
- 11.3Sum Rule6 Minutes
- 11.4Combining Sum and Product Rules5 Minutes
- 11.5Permutations and Combinations15 Minutes
- 11.6Permutations and Combinations with Repetition5 Minutes
- 11.7Principle of Inclusion-Exclusion4 Minutes
- 11.8Pigeonhole Principle10 Minutes
- 11.9Exercise on Pigeonhole Principle6 Minutes
- 11.10Indistinguishable Objects4 Minutes
- 11.11Binomial Theorem13 Minutes
- 11.12Binomial Theorem (2)2 Minutes
- 11.13Useful Identity5 Minutes
- Counting Exercises11
- Revision for Counting3
- Major II11
- Advanced Counting11
- 15.1Recurrence Relations3 Minutes
- 15.2Recurrence Relations (2)3 Minutes
- 15.3Degree of Recurrence Relations1 Minute
- 15.4Exercise on Recurrence Relations4 Minutes
- 15.5Homogeneous Recurrence Relations2 Minutes
- 15.6Solving Recurrence Relations7 Minutes
- 15.7Exercise on Solving Recurrence Relations4 Minutes
- 15.8General Rule for Recurrence Relations13 Minutes
- 15.9Solving Non-Homogeneous Recurrence Relations12 Minutes
- 15.10Exercise on Non-Homogeneous Recurrence Relations7 Minutes
- 15.11Generating Functions6 Minutes
- Relations11
- 16.1Relations21 Minutes
- 16.2Composition of Relations24 Minutes
- 16.3Composition Using Matrices5 Minutes
- 16.4Union and Intersection of Relations5 Minutes
- 16.5Equivalence Relations5 Minutes
- 16.6Proving Equivalence Relations10 Minutes
- 16.7Equivalence Classes11 Minutes
- 16.8Partial Ordering6 Minutes
- 16.9Total Ordering13 Minutes
- 16.10Hasse Diagram13 Minutes
- 16.11Hasse Diagram (2)3 Minutes
- Graphs (Not included this semester)10
- 17.1Graphs (Not included this semester)5 Minutes
- 17.2Graph Properties (Not included this semester)7 Minutes
- 17.3Special Graphs (Not included this semester)6 Minutes
- 17.4Regular Graphs (Not included this semester)8 Minutes
- 17.5Bipartite Graphs (Not included this semester)9 Minutes
- 17.6Representing Graphs (Not included this semester)4 Minutes
- 17.7Adjacency List (Not included this semester)1 Minute
- 17.8Isomorphism (Not included this semester)25 Minutes
- 17.9Graph Paths (Not included this semester)6 Minutes
- 17.10Connectivity (Not included this semester)4 Minutes
- Final10
- Live Sessions2
- RSA Cryptosystem Project (Girls)3
- Caesar Cipher Project (Boys)6
- DH RSA Project (Boys)5
Instructor
Instructor