CPES - CYCLE PLURISCIPLINAIRE D'ÉTUDES SUPÉRIEURES - MODELLING AND DIGITAL ECONOMICS

Program of the first year of mathematics at the Lycée Joffre

# Reasoning and set vocabulary

# Complements of algebraic calculus, elementary analysis and geometry

# Enumeration

# Real analysis: numerical sequences, limits and continuity, differentiability, calculus of primitives and integrals.

# Complex numbers

# Differential equations

# Linear algebra: vectors, linear maps and matrices, bases and dimension,

# Asymptotic analysis

# Basics of statistics

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This modern language teaching is based on the written and oral practice of English, with particular emphasis on the scientific or socio-economic context.

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The first-year program is as follows:

# Introduction to the problems of the contemporary world

# Introduction to economics Introduction to geopolitics

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The program below covers the two first-year computer science courses at the Lycée Joffre:

Algorithmics and Programming 1: Basic Concepts in Algorithmics and Programming:
• Notion of problem, problem instance, complexity, termination, proof of validity
• Algorithms and iterative processing
• Proof: validity, termination, complexity
• Linear structures: arrays, linked lists, stacks, queues
• Sorting: inserting, selecting, merging sorting, other sorting examples
• Introduction to recursive processing (dichotomous search, etc.)
• Python programming

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Use of computer systems: introduction to the main concepts of computer systems:
- Practical mastery of a Linux environment
- Knowledge of the main Linux commands
- Understanding of documentation pages (man)
- Sessions, files, directories, access rights
- Programs, processes, commands and command languages
- Console (terminal) vs. graphical execution mode
- Familiarization with shells, writing a few scripts

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Introduction to digital analysis 

# Basics, issues and limitations, representation of numbers in a machine

# Analytical add-ons for numerical analysis

# Numerical solution of nonlinear equations

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General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

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Synthetic program:

– Probabilistic vocabulary

– Random variables and probability distributions

– Expectation and variance

–Applications

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The first-year program is as follows:

# Introduction to the problems of the contemporary world

# Introduction to Economics

# Introduction to geopolitics

See full page

Program of the first year of mathematics at the Lycée Joffre

# Reasoning and set vocabulary

# Complements of algebraic calculus, elementary analysis and geometry

# Enumeration

# Real analysis: numerical sequences, limits and continuity, differentiability, calculus of primitives and integrals.

# Complex numbers

# Differential equations

# Linear algebra: vectors, linear maps and matrices, bases and dimension,

# Asymptotic analysis

# Basics of statistics

See full page

The program below covers the two first-year computer science courses at the Lycée Joffre:

Algorithmics and Programming 1: Basic Concepts in Algorithmics and Programming:
• Notion of problem, problem instance, complexity, termination, proof of validity
• Algorithms and iterative processing
• Proof: validity, termination, complexity
• Linear structures: arrays, linked lists, stacks, queues
• Sorting: inserting, selecting, merging sorting, other sorting examples
• Introduction to recursive processing (dichotomous search, etc.)
• Python programming

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VBA Programming in Excel Development of VBA Macros in Excel:

# Practice macros in Excel

# Application of the basics of the VBA language in Excel

# Debugging VBA macros in Excel

# Writing custom functions

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General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

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This modern language teaching is focused on the written and oral practice of English, with a particular emphasis on a scientific or socio-economic context.

See full page

Second year mathematics program, part taught at Lycée Joffre :

# Reminders of linear algebra and complements of Euclidean geometry

# Advanced probability

# Analysis of functions of one variable

# Functions of several variables

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This course continues the training of students in applied mathematics with a focus on numerical methods.

Program (may be modified depending on the year and the time available):

# Matrix Numerical Analysis

# Digital Integration

# numerical solution of diffential equations

# Introduction to the qualitative study of nonlinear differential equations

.

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This modern language teaching is focused on the written and oral practice of English, with a particular emphasis on oral expression.

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This course completes the training in computer science by opening up to the study of information systems and databases (design of processing in an information system and the management of relational databases):

# Information systems: introduction of the entity/association model, relational model, processing modeling (conceptual processing model, organizational processing model)

# Databases: creation, manipulation and querying of relational databases.

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Linear Algebra Complements, Reduction Theory, and Applications 

# Complements of linear algebra, the notion of direct sum

# Determinants

# Reduction: diagonalization and applications to the study of discrete and continuous dynamical systems in physics, chemistry, biology or economics.

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The 2nd year computer science course taught at the Lycée is focused on advanced concepts in algorithmics and programming:

# Tree data structures: binary trees, heaps, ABRs, priority queues

# Sort by heap, lower bound on sorting

# Graph structure: representations (adjacency matrices, edge lists, neighbor lists)

# Basic algorithms (connectedness, depth and width paths, topological sorting)

# Distance calculation (Dijkstra, heap implementation)

# Introduction to object programming (encapsulation, late binding, classes, methods, etc.)

# Programming in Python

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General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

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General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

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Introduction to the use of data mining methods:

# Motivations, areas of application

# Data mining tasks (classification, estimation, prediction, etc.)

# Processing on the data (pre/post-processing)

# Supervised learning (Bayes method, k nearest neighbors, neural networks, etc.)

# Unsupervised learning (k-means)

# Evaluation of methods

# Data mining software (R, Scikit, Weka, etc.)

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Second year mathematics program, part taught at Lycée Joffre :

# Reminders of linear algebra and complements of Euclidean geometry

# Advanced probability

# Analysis of functions of one variable

# Functions of several variables

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This course continues the training of students in applied mathematics, in particular the use of statistical tools:

# Notions of populations and random samples.

# Estimators.

#Erreur mean square and bias-variance decomposition.

# Empirical estimators of mean and variance. Construction of estimators by the method of moments. Maximum plausibility.
Interval estimation.

# Hypothesis tests: null hypothesis, alternative hypothesis. Errors of the first and second kinds. Power of a test. Test Statistic, Rejection Region. Examples of classic tests.

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The 2nd year computer science course taught at the Lycée is focused on advanced concepts in algorithmics and programming:

# Tree data structures: binary trees, heaps, ABRs, priority queues

# Sort by heap, lower bound on sorting

# Graph structure: representations (adjacency matrices, edge lists, neighbor lists)

# Basic algorithms (connectedness, depth and width paths, topological sorting)

# Distance calculation (Dijkstra, heap implementation)

# Introduction to object programming (encapsulation, late binding, classes, methods, etc.)

# Programming in Python

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This modern language teaching is focused on the written and oral practice of English, with a particular emphasis on oral expression.

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