Second-Year Bachelor's Degree in CPES: Modeling and Numerical Methods in the Life Sciences

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Second-year mathematics curriculum, portion taught at Lycée Joffre:

# Review of Linear Algebra and Additional Concepts in Euclidean Geometry

# Advanced Probability

# Further Analysis of Functions of a Single Variable

# Functions of Several Variables

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This course is a cross-disciplinary course in the second year of the SV program designed to provide biology students with a fundamental understanding of how plants function, enabling them to grasp the current challenges in plant agricultural sciences.

The following basic concepts of plant physiology and functional biology will be studied: 

Key experimental approaches: plant transgenesis, forward and reverse genetics

Fundamentals of Autotrophy

mechanisms underlying the major stages of angiosperm development: meristem function, floral transition, and fertilization.

auxin, a key hormone involved in plant development and their response to the abiotic environment

The laboratory sessions will allow students to experiment with regulating plant water uptake and to analyze plant mineral nutrition using various biochemical assays (flame photometry, spectrophotometry). 

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This course is an introduction to the general concepts of scientific ecology: levels of organization, measurement and conservation of biodiversity, biogeography, and biotic and abiotic factors influencing the distribution and dynamics of biodiversity. It also provides an understanding of the methods used in scientific ecology: the importance of experimentation, considerations for designing a protocol, data analysis, and oral and written reports on an experiment.

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Advanced Topics in Linear Algebra, Reduction Theory, and Applications 

# Additional Concepts in Linear Algebra: The Concept of Direct Sum

# Determinants

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

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This course continues to build students' skills in applied mathematics, with a focus on numerical methods.

Schedule (subject to change depending on the year and the time available):

# Matrix Numerical Analysis

# digital integration

# Numerical Solution of Differential Equations

# Introduction to the Qualitative Analysis of Nonlinear Differential Equations

.

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The 10th-grade computer science course offered at the high school focuses on advanced concepts in algorithms and programming:

# Tree Data Structures: Binary Trees, Heaps, ABR, Priority Queues

# Sorting into piles, lower bound on the sort

# Graph Structures: Representations (Adjacency Matrices, Edge Lists, Neighbor Lists)

# Basic Algorithms (Connectivity, Breadth-First and Depth-First Search, Topological Sorting)

# Distance Calculation (Dijkstra, Heap Implementation)

# Introduction to Object-Oriented Programming (encapsulation, late binding, classes, methods, etc.)

# Python Programming

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This course unit complements the computer science curriculum by introducing students to the study of information systems and databases (designing processes within an information system and managing relational databases):

# Information Systems: Introduction to the Entity-Relationship Model, the Relational Model, and Business Process Modeling (Conceptual Business Process Model, Organizational Business Process Model)

# Databases: Creating, Manipulating, and Querying Relational Databases.

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This module is designed to enable students to acquire:

Basic Concepts in Physiology: The concept of homeostasis; levels of organization in the human body; compartments of the internal environment; study of the endocrine system; acid-base and water-mineral balances; anatomical and functional studies of the central and peripheral nervous systems.

Basic Concepts in Immunology:

General overview of the immune system; study of T and B lymphocytes and antigen-presenting cells; study of antimicrobial immunity and the complement system.

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This modern language course focuses on the written and spoken use of English, with a particular emphasis on speaking.

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The EU covers the theoretical concepts of plant biology, using the group of spermatophytes as a model. It aims to define the concepts and specific vocabulary related to morphology, anatomy, reproduction, and life cycles.

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The EU is interested in describing the morpho-anatomical characteristics of the major organizational plans of metazoans found in present-day and past faunas, as well as in explaining their origin and the dynamics of their emergence. It thus develops a perspective on organisms based on paleontology and zoology. It will primarily address the origin of metazoans and the main divisions—diploblastic and triploblastic organisms—as well as basic concepts related to the positioning and phylogenetic relationships among taxa (mono- and paraphyly, evolutionary convergence, etc.). The course is traditionally divided into lectures, tutorials—which will primarily aim to illustrate and support aspects related to the biodiversity of taxa—and laboratory sessions designed to develop skills, particularly and mandatorily in dissection.

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General Knowledge (Epistemology and Philosophy):

# History of Ideas

# Epistemology of Science and Digital Technology

#Argumentation and Communication

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Second-year mathematics curriculum, portion taught at Lycée Joffre:

# Review of Linear Algebra and Additional Concepts in Euclidean Geometry

# Advanced Probability

# Further Analysis of Functions of a Single Variable

# Functions of Several Variables

View the full page

This course is a cross-disciplinary course in the second year of the SV program designed to provide biology students with a fundamental understanding of how plants function, enabling them to grasp the current challenges in plant agricultural sciences.

The following basic concepts of plant physiology and functional biology will be studied: 

Key experimental approaches: plant transgenesis, forward and reverse genetics

Fundamentals of Autotrophy

mechanisms underlying the major stages of angiosperm development: meristem function, floral transition, and fertilization.

auxin, a key hormone involved in plant development and their response to the abiotic environment

The laboratory sessions will allow students to experiment with regulating plant water uptake and to analyze plant mineral nutrition using various biochemical assays (flame photometry, spectrophotometry). 

View the full page

This course is an introduction to the general concepts of scientific ecology: levels of organization, measurement and conservation of biodiversity, biogeography, and biotic and abiotic factors influencing the distribution and dynamics of biodiversity. It also provides an understanding of the methods used in scientific ecology: the importance of experimentation, considerations for designing a protocol, data analysis, and oral and written reports on an experiment.

View the full page

Advanced Topics in Linear Algebra, Reduction Theory, and Applications 

# Additional Concepts in Linear Algebra: The Concept of Direct Sum

# Determinants

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

View the full page

This course continues to build students' skills in applied mathematics, with a focus on numerical methods.

Schedule (subject to change depending on the year and the time available):

# Matrix Numerical Analysis

# digital integration

# Numerical Solution of Differential Equations

# Introduction to the Qualitative Analysis of Nonlinear Differential Equations

.

View the full page

The 10th-grade computer science course offered at the high school focuses on advanced concepts in algorithms and programming:

# Tree Data Structures: Binary Trees, Heaps, ABR, Priority Queues

# Sorting into piles, lower bound on the sort

# Graph Structures: Representations (Adjacency Matrices, Edge Lists, Neighbor Lists)

# Basic Algorithms (Connectivity, Breadth-First and Depth-First Search, Topological Sorting)

# Distance Calculation (Dijkstra, Heap Implementation)

# Introduction to Object-Oriented Programming (encapsulation, late binding, classes, methods, etc.)

# Python Programming

View the full page

This course unit complements the computer science curriculum by introducing students to the study of information systems and databases (designing processes within an information system and managing relational databases):

# Information Systems: Introduction to the Entity-Relationship Model, the Relational Model, and Business Process Modeling (Conceptual Business Process Model, Organizational Business Process Model)

# Databases: Creating, Manipulating, and Querying Relational Databases.

View the full page

This module is designed to enable students to acquire:

Basic Concepts in Physiology: The concept of homeostasis; levels of organization in the human body; compartments of the internal environment; study of the endocrine system; acid-base and water-mineral balances; anatomical and functional studies of the central and peripheral nervous systems.

Basic Concepts in Immunology:

General overview of the immune system; study of T and B lymphocytes and antigen-presenting cells; study of antimicrobial immunity and the complement system.

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This modern language course focuses on the written and spoken use of English, with a particular emphasis on speaking.

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General Knowledge (Epistemology and Philosophy):

# History of Ideas

# Epistemology of Science and Digital Technology

#Argumentation and Communication

View the full page

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Second-year mathematics curriculum, portion taught at Lycée Joffre:

# Review of Linear Algebra and Additional Concepts in Euclidean Geometry

# Advanced Probability

# Further Analysis of Functions of a Single Variable

# Functions of Several Variables

View the full page

General Knowledge (Epistemology and Philosophy):

# History of Ideas

# Epistemology of Science and Digital Technology

#Argumentation and Communication

View the full page

Introduction to the Use of Data Mining Methods:

# Motivations, Areas of Application

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

# Data Processing (Pre- and Post-Processing)

# Supervised learning (Bayesian 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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The “Physiology of Major Body Functions” course in the fourth semester of the CPES program is designed to complement the course devoted to the study of the roles and interactions of the body’s various systems that work together to maintain a constant internal environment. This course is taught through laboratory sessions and tutorials.

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This course continues to provide students with training in applied mathematics, particularly in the use of statistical tools:

# Concepts of Populations and Random Samples.

# Estimators.

#Mean Square Error and Bias-Variance Decomposition.

# Empirical estimators of the mean and variance. Construction of estimators using the method of moments. Maximum likelihood.
Interval estimation.

# Hypothesis testing: null hypothesis, alternative hypothesis. Type I and Type II errors. Test power. Test statistic, rejection region. Examples of classic tests.

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The objective of this course unit is to understand evolutionary processes at both the micro- and macro-evolutionary scales.

Using examples, hands-on activities, and accessible modeling, the course will aim to present, in a concrete and quantitative way, the effects of the four evolutionary forces operating at the individual and population levels (mutation, migration, selection, and genetic drift). The integration of these microevolutionary processes into larger timescales (e.g., lineage differentiation, speciation) will then be addressed. Finally, the course unit will include an introduction to phylogenetic tools (interpreting and constructing phylogenetic trees) that enable the study of macroevolutionary events (diversification, extinction) and the tracing of changes in character states, particularly by incorporating fossil data.

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- Physiology of Major Body Systems: Anatomy and Functions of the Cardiovascular, Respiratory, Renal, and Digestive Systems.

- Cellular and Molecular Biology 3: cytoskeletal function, cell adhesion, protein trafficking and methods of study, cell cycle regulation, immunoprecipitation, fluorescence video microscopy, RNA interference, overexpression, regulation of gene expression: transcriptional regulation (repressors, activators) and attenuation in prokaryotes, mechanisms of expression regulation in eukaryotes.

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The 10th-grade computer science course offered at the high school focuses on advanced concepts in algorithms and programming:

# Tree Data Structures: Binary Trees, Heaps, ABR, Priority Queues

# Sorting into piles, lower bound on the sort

# Graph Structures: Representations (Adjacency Matrices, Edge Lists, Neighbor Lists)

# Basic Algorithms (Connectivity, Breadth-First and Depth-First Search, Topological Sorting)

# Distance Calculation (Dijkstra, Heap Implementation)

# Introduction to Object-Oriented Programming (encapsulation, late binding, classes, methods, etc.)

# Python Programming

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This modern language course focuses on the written and spoken use of English, with a particular emphasis on speaking.

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This required course will enable students to build on the skills they acquired in “Biochemistry S3.” It will help them understand cellular metabolism by:

-an understanding of bioenergetics in order to study the processes by which living cells transport, transmit, utilize, store, and release energy;
-the study of the catabolism and anabolism of carbohydrates, lipids, nucleotides, and amino acids, as well as the metabolic interactions between these pathways.

- a description of metabolic disorders.

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In this introductory course on genetic analysis, the objectives are to become familiar with the terminology, principles, concepts, and methods used in formal genetics, as well as their applications, particularly in human and medical genetics. This course covers the genetics of inheritance (Mendelian and non-Mendelian), quantitative genetics, and basic concepts of population genetics. Throughout the course, close connections are drawn between classical genetics and molecular genetics.

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This course unit aims to expand on previously acquired knowledge in various fields of microbiology, particularly microbial ecology.

It will cover pathogenic relationships, but will also present examples of symbiotic associations. It will address the applications of microorganisms in biotechnology. It will describe how antibiotics work and the associated resistance phenomena, as well as their impact.

The EU will address the concept of viral ecology by presenting the place and role of viruses in ecosystems. Bacteriophages will be discussed in greater detail, and the mechanisms by which bacteria resist phage infection will be explained. The various types of viral infections in animals will be presented (acute and persistent infections) and illustrated through the study of the pathogenesis of selected viral infections.

Knowledge of microorganisms will be expanded through the study of archaea and a model eukaryotic organism, yeast.

The lab sessions will focus on performing and interpreting an antibiogram, and on titrating bacteriophages.

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This course, similar in spirit to the first-year project, is an introduction to the research process that goes deeper than the first-year course: it includes immersion in a research laboratory, a literature review, and the completion of a project involving the study of a biological context, the collection of experimental or observational data, and the implementation of a modeling and/or numerical simulation approach.

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Second-year mathematics curriculum, portion taught at Lycée Joffre:

# Review of Linear Algebra and Additional Concepts in Euclidean Geometry

# Advanced Probability

# Further Analysis of Functions of a Single Variable

# Functions of Several Variables

View the full page

General Knowledge (Epistemology and Philosophy):

# History of Ideas

# Epistemology of Science and Digital Technology

#Argumentation and Communication

View the full page

Introduction to the Use of Data Mining Methods:

# Motivations, Areas of Application

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

# Data Processing (Pre- and Post-Processing)

# Supervised learning (Bayesian 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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The course builds on the L2 S3 course, focusing on describing the morpho-anatomical characteristics of the major organizational levels of metazoans found in present-day and past faunas, as well as explaining their origin and the dynamics of their emergence through the acquisition of skills in paleontology and zoology. In S4, the course will primarily explore the major subdivisions within protostome organisms—namely the Lophotrochozoa (annelids, mollusks, brachiopods, etc.) and the Ecdysozoa (arthropods, nematodes, etc.)—while emphasizing their phylogenetic relationships as well as their socio-economic significance and impacts. The course unit is traditionally divided into lectures, tutorials—which will primarily aim to illustrate and support aspects related to the biodiversity of taxons—and laboratory sessions designed to develop skills, notably and mandatorily through the performance of certain dissections.

View the full page

This course continues to provide students with training in applied mathematics, particularly in the use of statistical tools:

# Concepts of Populations and Random Samples.

# Estimators.

#Mean Square Error and Bias-Variance Decomposition.

# Empirical estimators of the mean and variance. Construction of estimators using the method of moments. Maximum likelihood.
Interval estimation.

# Hypothesis testing: null hypothesis, alternative hypothesis. Type I and Type II errors. Test power. Test statistic, rejection region. Examples of classic tests.

View the full page

The objective of this course unit is to understand evolutionary processes at both the micro- and macro-evolutionary scales.

Using examples, hands-on activities, and accessible modeling, the course will aim to present, in a concrete and quantitative way, the effects of the four evolutionary forces operating at the individual and population levels (mutation, migration, selection, and genetic drift). The integration of these microevolutionary processes into larger timescales (e.g., lineage differentiation, speciation) will then be addressed. Finally, the course unit will include an introduction to phylogenetic tools (interpreting and constructing phylogenetic trees) that enable the study of macroevolutionary events (diversification, extinction) and the tracing of changes in character states, particularly by incorporating fossil data.

View the full page

- Physiology of Major Body Systems: Anatomy and Functions of the Cardiovascular, Respiratory, Renal, and Digestive Systems.

- Cellular and Molecular Biology 3: cytoskeletal function, cell adhesion, protein trafficking and methods of study, cell cycle regulation, immunoprecipitation, fluorescence video microscopy, RNA interference, overexpression, regulation of gene expression: transcriptional regulation (repressors, activators) and attenuation in prokaryotes, mechanisms of expression regulation in eukaryotes.

View the full page

The 10th-grade computer science course offered at the high school focuses on advanced concepts in algorithms and programming:

# Tree Data Structures: Binary Trees, Heaps, ABR, Priority Queues

# Sorting into piles, lower bound on the sort

# Graph Structures: Representations (Adjacency Matrices, Edge Lists, Neighbor Lists)

# Basic Algorithms (Connectivity, Breadth-First and Depth-First Search, Topological Sorting)

# Distance Calculation (Dijkstra, Heap Implementation)

# Introduction to Object-Oriented Programming (encapsulation, late binding, classes, methods, etc.)

# Python Programming

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The EU addresses the various groups of plants (“algae,” “cryptogams,” and spermatophytes”), specifying for each group its phylogenetic position and nature (monophyletic or paraphyletic), its origin, and its distinctive features in terms of morphology, anatomy, reproduction, and ecology.

The 4th-grade classes cover the different groups of plants: 4th grade, diversity of “algae”; 5th grade, life cycles of “algae”; 6th grade, “cryptogams”; 7th grade, spermatophytes.

Six tutorials cover cross-cutting concepts through oral and written exercises: Tutorial 1, Biological Cycles; Tutorial 2, Endosymbiosis; Tutorial 3, Interactions; Tutorial 4, Adaptation; Tutorial 5, Polyploidy; Tutorial 6, Phylogeny.

Six lab sessions illustrate the concepts covered in lectures and tutorials using living specimens: Lab 1, “Algae” 1; Lab 2, “Algae” 2; Lab 3, “Bryophytes”; Lab 4, “Pteridophytes”; Lab 5, Gymnosperms, vegetative system; Lab 6, Gymnosperms, reproduction.

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The Functional Ecology course aims to provide a solid foundation in the functioning of terrestrial ecosystems, with a particular focus on the role played by living organisms in material flows within these ecosystems. The main processes covered are primary production, consumer relationships—particularly herbivory—and the decomposition and transformation of soil organic matter. For each of these processes, special attention is given to (1) the link between organisms’ strategies and their function within the ecosystem, and (2) basing the presentation of concepts on field observations, highlighting characteristics of organisms or the ecosystem that students might encounter during field trips.

This course thus bridges a broader introduction to ecology in the first semester (HLBE304) and introduces concepts necessary for the third-year course on community ecology.

The focus is on practical aspects, particularly through a series of group-based hands-on activities, in which a simple but scientifically relevant hypothesis will be tested experimentally using an appropriate protocol.

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This modern language course focuses on the written and spoken use of English, with a particular emphasis on speaking.

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This course, similar in spirit to the first-year project, is an introduction to the research process that goes deeper than the first-year course: it includes immersion in a research laboratory, a literature review, and the completion of a project involving the study of a biological context, the collection of experimental or observational data, and the implementation of a modeling and/or numerical simulation approach.

View the full page