Introduction to Algebra (M1100)

For first-year students in Mathematics, Statistics, Computer Science, Physics, and Electronics, Lebanese University, Faculty of Sciences M1100 is where university mathematics begins. It's usually the first course that asks you to prove things rather than just compute them, and many students struggle with that shift. This course walks you through the entire syllabus step by step, so you understand the definitions, know how to write clean proofs, and can handle the exercises you'll face in exams. How the course works Recorded lessons: Every chapter is explained in clear, structured videos. You can watch at your own pace, pause, and rewatch before exams. Live sessions: Regular live classes where we solve exercises together, go over common exam questions, and answer your questions directly. Exercise-focused: We work through the official chapter exercises and exam-style problems, not just the theory. What you'll learn Logic and set theory: Statements, truth tables, quantifiers and their negations, types of proof (direct, contraposition, contradiction, induction), sets, operations on sets, De Morgan's laws, Cartesian products, and families of sets. Mappings: Composition, direct and inverse images, and injective, surjective, bijective, and invertible mappings. Finite sets: Equipollent sets, cardinality, and counting results for unions, subsets, and power sets. Binary operations: Associativity, commutativity, distributivity, neutral and invertible elements, monoids, induced laws, and homomorphisms. Groups, rings, and fields: Subgroups, group homomorphisms, kernel and image, rings, subrings, fields, and subfields. Complex numbers: Algebraic, trigonometric, and exponential forms, modulus and argument, De Moivre's formula, n-th roots, roots of unity, and solving quadratic equations in ℂ. Polynomials: Operations, degree, Euclidean division, Horner's method, roots and multiplicity, derivatives, Taylor's formula, irreducible polynomials, and factorization over ℝ and ℂ. By the end of the course, you will be able to: Read and write rigorous mathematical proofs with confidence Solve the standard M1100 exercise types (sets, mappings, groups, complex numbers, polynomials) Approach exam questions methodically instead of memorizing solutions Who it's for This course is for first-year Faculty of Sciences students taking M1100.