DisCont mathematics 1
The course enables students to a deeper understanding of the basic modern mathematical structures, mainlz in the field of discrete mathematics, combinatorics, number theory and analysis of algorithms.
- Understand the principles and analysis of complex algorithms.
- Apply the technique of recursive relations, in various situations.
- Apply complex terchniques of calculations of finite sums.
- Analyse the complexity of an algortihm.
- Undersand the connection between various mathematical structures.
- Use the technique of generating functions in various situations.
- Understand the principles of cyphers and coding.
- Analyze the principles of sorting and searching algorithms.
Forms of Teaching
Lectures are organized through two cycles. The first cycle consists of 7 weeks of classes and mid-term exam, a second cycle of 6 weeks of classes and final exam. Classes are conducted through a total of 15 weeks with a weekly load of 4 hours.Exams
Mid-term exam in the 8th week of classes and final exam in the 15th week of classes.Consultations
Consultations are held one hour weekly according to arrangement with students.
|Type||Threshold||Percent of Grade||Comment:||Percent of Grade|
|Homeworks||0 %||20 %||0 %||20 %|
|Class participation||0 %||2 %||0 %||10 %|
|Seminar/Project||0 %||20 %||0 %||20 %|
|Mid Term Exam: Written||0 %||40 %||0 %|
|Final Exam: Written||0 %||40 %|
|Exam: Written||0 %||80 %|
Week by Week Schedule
- Introductory example - The Tower of Hanoi
- Finite sums
- Binomial coefficients. Combinatorial identities
- Walks on integer latices. Generating functions.
- Binomial series. Polynomial formulae. Increasing and decreasing factoriels. Finite differences.
- Recursions. Sequences given by recursive formulas. Examples.
- Fibonacci numbers.
- Euler and Stirling numbers. Sum of powers. Bernoulli numbers.
- Elementary inequalities.
- Means. Inequality between means. Symmetric functions.
- Euclid's algorithm, divisibility. Relatively prime numbers. Congruences.
- Prime numbers. Fermat's and Wilson's Theorem. Applications.
- Basic search and sorting algorithms and their complexity.