Title ΣΕΜΙΝΑΡΙΟ ΠΡΟΒΛΗΜΑΤΩΝ ΙΙ / SEMINARIO PROVLĪMATŌN II Code 0148 Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Spring Coordinator Romanos diogenis Malikiosis Common No Status Active Course ID 600017209

### Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 12
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses212

 Academic Year 2019 – 2020 Class Period Spring Faculty Instructors Weekly Hours 2 Class ID 600147675
Type of the Course
• Scientific Area
• Skills Development
Course Category
Knowledge Deepening / Consolidation
Mode of Delivery
• Face to face
Digital Course Content
Language of Instruction
• Greek (Instruction)
• English (Instruction, Examination)
General Competences
• Work in an international context
• Advance free, creative and causative thinking
Course Content (Syllabus)
Analysis 1. Real and complex numbers. 2. Sequences and series of numbers. 3. Functions of one real variable: continuity, differentiability, Taylor formula, Riemann integral. 4. Sequences and series of functions: pointwise and uniform convergence; differentiability and integrability term by term. 5. Power series, elementary functions. 6. Improper Riemann integral, functions defined by integrals (Euler integrals). 7. Solution of ordinary differential equations 8. Multivariate functions. Fubini-Tonelli theorem. Theorems of Green, Stokes, Gauss. 9. Lebesgue integral. Monotone and dominated convergence theorem. Algebra and Geometry 1. General notions about some algebraic structures: groups, rings, fields. 2. General properties about polynomials with real and complex coefficients. 3. Finite dimensional vector spaces over real and complex numbers: base and dimension. 4. Linear transformations and matrices; eigenvalues, eigenvectors, diagonal form and applications. 5. Quadratic forms. Plane and and solid analytical geometry: lines, planes, conics, quadrics. Number Theory 1. Divisibility, congruences modn. 2. Theorems of Fermat, Euler, Wilson. 3. Quadratic residues. Multiplicative structure of reduced residues modn. Probability and Combinatorics 1. Random walks on the plane and space. 2. Geometric probability. 3. Generating functions.
Educational Material Types
• Notes
• Book
Course Organization