Mathematics

ALESSANDRO PANCONESI
CLAUDIO CILLI

General objectives

Acquire basic knowledge on the design of basic algorithms, iterative and recursive algorithms, and the computation of their computational efficiency.

Specific objectives

Knowledge and understanding:
At the end of the course students will know the basic methodologies for the design and analysis of iterative and recursive algorithms, the main data structures, some ways to explore such structures, the main sorting algorithms and the most basic implementations of the dictionaries. They will have a good knowledge of the C language, including advanced aspects such as dynamic memory allocation, pointer arithmetic and separate program compilation.

Apply knowledge and understanding:
At the end of the course students will have become familiar with the main basic data structures, in particular those implementing dictionaries. They will be able to explain the algorithms and analyze their time complexity, highlighting how their performances depend on the used data structure. They will be able to design new data structures and related algorithms, on the basis of the existing ones; they will be able to explain the main sorting algorithms, illustrating the underlying design strategies and their time complexity analysis; they will be able to compare the asymptotic behavior of the execution times of the studied algorithms, to design recursive solutions to problems and to analyze their asymptotic time complexity. Finally, they will be able to implement the learned algorithms and data structures in the C language, with attention also to the correctness, clarity and concrete efficiency of the programs.


Critical and judgmental skills:
Students will be able to analyze the quality of an algorithm and related data structures, both from the effective resolution of the problem and from the time complexity point of views.

Communication skills:
Students will acquire the ability to expose their knowledge in a clear and organized way, which will be verified both through the written tests and during the oral examination.
Students will be able to express an algorithmic idea rigorously both at high level, through the use of the pseudocode, and in the C language.

Learning ability:
Once the cycle of studies is completed, the acquired knowledge will allow students to face the study of algorithmic techniques, of more advanced data structures and of advanced programming methodologies within a master's degree course.

Design, analysis and implementation of basic algorithms and data structures

Prerequisites for the course are familiarity with the basics of any modern high-level programming language, in particular of C / C ++, which are provided in the course Programming and Calculation Laboratory (LPC), a compulsory first-year course of the Mathematics degree curriculum.

General part (60 hours):
Description and design of efficient algorithms: Introduction to the concepts of algorithm, data structure, efficiency, computational complexity. Asymptotic notation. Introduction to recursion. The problem of sorting. Basic data structures (arrays, lists, stacks, queues, priority queues, trees). Dictionaries. Graphs.

Coding module (30 hours):
The C programming language: Principles of good programming (structured programming, development of correct codes following a top-down methodology by structuring code with use of functions). C basics: iterative constructs and functions, vectors and structures. Recursion in C. Pointers and dynamic memory allocation. Fundamental data structures such as lists, stacks and binary trees.

Reference text:
Jon Kleinberg and Eva Tardos, Algorithm design

Lecture notes and other material may be provided by the instructor when appropriate

Besides lectures in class for the core material and the coding module (for about 70% and 30% of the time, respectively), non-mandatory tutoring in the coding lab is provided, so that students can individually develop programs supported by a tutor.

The exam aims at evaluating what students have learned through a written test (consisting in solving problems of the same type as those discussed in class), and a coding project (consisting in writing and running C programs of varying difficulty). The written test can be replaced by two intermediate tests, the first of which (midterm) takes place at about mid-course and the second one immediately after the end of the course. The midterm focuses on the topics covered so far, while the second on the topics covered in the remaining.