Course description

Title of the Teaching Unit

Advanced Mathematics and Statistics 2

Code of the Teaching Unit

12UMQ30

Academic year

2024 - 2025

Cycle

Number of credits

Number of hours

Quarter

Weighting

Site

Anjou

Teaching language

French

Teacher in charge

ENGELBEEN Céline

Objectives and contribution to the program

The aim is to create in the student a sufficiently broad mathematical culture to enable him/her to approach serenely the quantitative problems that he/she is likely to encounter in his/her professional life.
At the end of the undergraduate advanced mathematics courses, the student should be able to :
- to apprehend the numerous management disciplines that call upon mathematical tools, including in the field of production management and in the technical field,
- to assimilate new quantitative techniques that he may be required to use during his career (particularly those related to the quantitative aspects raised by sustainability issues),
- to realize that a problem encountered is likely to receive a solution that uses mathematical tools, and to integrate, if necessary, into an internal or external team responsible for solving the problem,
- to grasp the meaning and scope of the very numerous publications in the field of management that make use of mathematical tools, to make a critical judgment on these publications and, where appropriate, to transpose or contribute to transposing the proposed solutions within the framework of the organization of which he or she is a member,
- to pursue, where appropriate, complementary studies or engage in research activities, including in areas of management where mathematical tools play an important role.
More generally, mathematics constitutes a formal language whose knowledge imposes and promotes the structuring of reasoning, from the level of elementary logic to techniques for reasoning in the uncertain.

Prerequisites and corequisites

The following "UE" are corequisite:
- Advanced Mathematics 1 and 2
- Advanced Mathematics and Statistics 1

Content

For the "Mathématiques approfondies" part, the course consists of four chapters :
- Chapter 1: Introduction
- Chapter 2: First-order differential equations
- Chapter 3: The differential equations of the second and higher order 2
- Chapter 4: First and second order recurrence equations

For the statistical part, the course consists of the following chapters:
- Chapter 1: Point estimation for means, proportions and variances.
- Chapter 2: The construction of confidence intervals for a mean and a proportion.
- Chapter 3: The construction of hypothesis tests for a mean, a variance, a comparison of means in independent and paired samples, a comparison of variances.
- Chapter 4: Chi-square tests.

Teaching methods

Type of teaching: ex cathedra plus exercise sessions.
The course alternates theoretical presentations and exercises designed to facilitate the assimilation of the notions introduced.
A series of exercises is proposed after each chapter. The home resolution of these exercises plays an important role in the assimilation of the subject matter; they allow the student to evaluate his or her degree of mastery of the subject matter taught and are the privileged instrument of preparation for the exam.
More generally, it should be emphasized that the working method must be based on reflection: memorization is not enough. It is essential not to allow any misunderstanding to pass: any statement must be able to be explained or justified. The student will only be able to achieve such a result through regular and in-depth work, which will take time but will allow him/her to acquire a structured mind.

The course will be given face-to-face. However, some sessions may be delivered remotely.

Assessment method

For the mathematical part :
Precision and comprehension are the essential criteria for scoring. Rigor and creativity are essential to pass the exam.

For the statistical part, the exam covers exercises at similar levels to those covered in the course. These exercises call for an in-depth understanding of the student.

Both exams will be face-to-face written exams.

References

Alpha C. Chiang, Fundamental methods of mathematical economics, 3rd edition, Mc Graw Hill, 1984.
This work can be considered as representative of the level of requirement of the course. Many chapters of the course are the subject of a presentation quite similar to the one found in this book. Its reading can therefore be recommended to the student.