Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts

A deep understanding of AI large language model mechanisms



A deep understanding of AI large language model mechanisms

A deep understanding of AI large language model mechanisms - 
Build and train LLM NLP transformers and attention mechanisms (PyTorch). Explore with mechanistic interpretability tools

Preview This Course - GET COUPON CODE

Description

Deep Understanding of Large Language Models (LLMs): Architecture, Training, and Mechanisms


Description

Large Language Models (LLMs) like ChatGPT, GPT-4, , GPT5, Claude, Gemini, and LLaMA are transforming artificial intelligence, natural language processing (NLP), and machine learning. But most courses only teach you how to use LLMs. This 90+ hour intensive course teaches you how they actually work — and how to dissect them using machine-learning and mechanistic interpretability methods.

This is a deep, end-to-end exploration of transformer architectures, self-attention mechanisms, embeddings layers, training pipelines, and inference strategies — with hands-on Python and PyTorch code at every step.

Whether your goal is to build your own transformer from scratch, fine-tune existing models, or understand the mathematics and engineering behind state-of-the-art generative AI, this course will give you the foundation and tools you need.


What You’ll Learn

    The complete architecture of LLMs — tokenization, embeddings, encoders, decoders, attention heads, feedforward networks, and layer normalization

    Mathematics of attention mechanisms — dot-product attention, multi-head attention, positional encoding, causal masking, probabilistic token selection

    Training LLMs — optimization (Adam, AdamW), loss functions, gradient accumulation, batch processing, learning-rate schedulers, regularization (L1, L2, decorrelation), gradient clipping

    Fine-tuning and prompt engineering for downstream NLP tasks, system-tuning

    Evaluation metrics — perplexity, accuracy, and benchmark datasets such as MAUVE, HellaSwag, SuperGLUE, and ways to assess bias and fairness

    Practical PyTorch implementations of transformers, attention layers, and language model training loops, custom classes, custom loss functions

    Inference techniques — greedy decoding, beam search, top-k sampling, temperature scaling

    Scaling laws and trade-offs between model size, training data, and performance

    Limitations and biases in LLMs — interpretability, ethical considerations, and responsible AI

    Decoder-only transformers

    Embeddings, including token embeddings and positional embeddings

    Sampling techniques — methods for generating new text, including top-p, top-k, multinomial, and greedy


Why This Course Is Different

    93+ hours of HD video lectures — blending theory, code, and practical application

    Code challenges in every section — with full, downloadable solutions

    Builds from first principles — starting from basic Python/Numpy implementations and progressing to full PyTorch LLMs

    Suitable for researchers, engineers, and advanced learners who want to go beyond “black box” API usage

    Clear explanations without dumbing down the content — intensive but approachable

Who Is This Course For?

    Machine learning engineers and data scientists

    AI researchers and NLP specialists

    Software developers interested in deep learning and generative AI

    Graduate students or self-learners with intermediate Python skills and basic ML knowledge

Technologies & Tools Covered

    Python and PyTorch for deep learning

    NumPy and Matplotlib for numerical computing and visualization

    Google Colab for free GPU access

    Hugging Face Transformers for working with pre-trained models

    Tokenizers and text preprocessing tools

    Implement Transformers in PyTorch, fine-tune LLMs, decode with attention mechanisms, and probe model internals

What if you have questions about the material?

This course has a Q&A (question and answer) section where you can post your questions about the course material (about the maths, statistics, coding, or machine learning aspects). I try to answer all questions within a day. You can also see all other questions and answers, which really improves how much you can learn! And you can contribute to the Q&A by posting to ongoing discussions.


By the end of this course, you won’t just know how to work with LLMs — you’ll understand why they work the way they do, and be able to design, train, evaluate, and deploy your own transformer-based language models.

Enroll now and start mastering Large Language Models from the ground up.

Who this course is for:


  •     AI engineers
  •     Scientists interested in modern autoregressive modeling
  •     Natural language processing enthusiasts
  •     Students in a machine-learning or data science course
  •     Graduate students or self-learners
  •     Undergraduates interested in large language models
  •     Machine-learning or data science practitioners
  •     Researchers in explainable AI

Linear Algebra and Geometry 1

Linear Algebra and Geometry 1

Systems of equations, matrices, determinants, vectors, and geometry of straight lines and planes in the 3-space


Linear Algebra and Geometry 1

Systems of equations, matrices, vectors, and geometry



Chapter 1: Systems of linear equations



S1. Introduction to the course

S2. Some basic concepts

You will learn: some basic concepts that will be used in this course. Most of them are known from high-school courses in mathematics, some of them are new; the latter will appear later in the course and will be treated more in depth then.

S3. Systems of linear equations; building up your geometrical intuition

You will learn: some basic concepts about linear equations and systems of linear equations; geometry behind systems of linear equations.

S4. Solving systems of linear equations; Gaussian elimination

You will learn: solve systems of linear equations using Gaussian elimination (and back-substitution) and Gauss--Jordan elimination in cases of systems with unique solutions, inconsistent systems, and systems with infinitely many solutions (parameter solutions).

S5. Some applications in mathematics and natural sciences

You will learn: how systems of linear equations are used in other branches of mathematics and in natural sciences.



Chapter 2: Matrices and determinants



S6. Matrices and matrix operations

You will learn: the definition of matrices and their arithmetic operations (matrix addition, matrix subtraction, scalar multiplication, matrix multiplication). Different kinds of matrices (square matrices, triangular matrices, diagonal matrices, zero matrices, identity matrix).

S7. Inverses; Algebraic properties of matrices

You will learn: use matrix algebra; the definition of the inverse of a matrix.

S8. Elementary matrices and a method for finding A inverse

You will learn: how to compute the inverse of a matrix with Gauss-Jordan elimination (Jacobi’s method).

S9. Linear systems and matrices

You will learn: about the link between systems of linear equations and matrix multiplication.

S10. Determinants

You will learn: the definition of the determinant; apply the laws of determinant arithmetics, particularly the multiplicative property and the expansion along a row or a column; solving equations involving determinants; the explicite formula for solving of n-by-n systems of linear equations (Cramer's rule), the explicite formula for inverse to a non-singular matrix.



Chapter 3: Vectors and their products



S11. Vectors in 2-space, 3-space, and n-space

You will learn: apply and graphically illustrate the arithmetic operations for vectors in the plane; apply the arithmetic operations for vectors in R^n.

S12. Distance and norm in R^n

You will learn: compute the distance between points in R^n and norms of vectors in R^n, normalize vectors.

S13. Dot product, orthogonality, and orthogonal projections

You will learn: definition of dot product and the way you can use it for computing angles between geometrical vectors.

S14. Cross product, parallelograms and parallelepipeds

You will learn: definition of cross product and interpretation of 3-by-3 determinants as the volume of a parallelepiped in the 3-space.



Chapter 4: Analytical geometry of lines and planes



S15. Lines in R^2

You will learn: several ways of describing lines in the plane (slope-intercept equation, intercept form, point-vector equation, parametric equation) and how to compute other kinds of equations given one of the equations named above.

S16. Planes in R^3

You will learn: several ways of describing planes in the 3-spaces (normal equation, intercept form, parametric equation) and how to compute other kinds of equations given one of the equations named above.

S17. Lines in R^3

You will learn: several ways of describing lines in the 3-space (point-vector equation, parametric equation, standard equation) and how to compute other kinds of equations given one of the equations named above.

S18. Geometry of linear systems; incidence between lines and planes

You will learn: determine the equations for a line and a plane and how to use these for computing intersections by solving systems of equations.

S19. Distance between points, lines, and planes

You will learn: determine the equations for a line and a plane and how to use these for computing distances.

S20. Some words about the next course

You will learn: about the content of the second course.



S21. Extras

You will learn: about all the courses we offer. You will also get a glimpse into our plans for future courses, with approximate (very hypothetical!) release dates.



Make sure that you check with your professor what parts of the course you will need for your final exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.



A detailed description of the content of the course, with all the 222 videos and their titles, and with the texts of all the 175 problems solved during this course, is presented in the resource file

“001 Outline_Linear_Algebra_and_Geometry_1.pdf”

under video 1 ("Introduction to the course"). This content is also presented in video 1.

Who this course is for:
  • University and college engineering

Become a Calculus 2 Master

become-calculus-2-master
Become a Calculus 2 Master, Learn everything from Calculus 2, then test your knowledge with 830+ practice questions

Created by Krista King, English [Auto-generated], Indonesian [Auto-generated], 5 more

Preview This Course - GET COUPON CODE

Workshop in Probability and Statistics

Workshop in Probability and Statistics
Workshop in Probability and Statistics, This workshop will teach you the fundamentals of statistics in order to give you a leg up at work or in school.
  • Created by George Ingersoll
  • English
  • English, French [Auto-generated], 6 more


PREVIEW THIS COURSE - GET COUPON CODE

What you'll learn
  • By the end of this workshop you should be able to pass any introductory statistics course
  • This workshop will teach you probability, sampling, regression, and decision analysis
  • Requirements
  • Knowledge of basic algebra
  • Microsoft Excel (recommended)

Curso completo de Estadística a nivel universitario

curso-completo-de-estadistica-a-nivel-universitario
Curso completo de Estadística a nivel universitario, Probabilidades, descriptiva univariada y bivariada, distribuciones, estimación, inferencia, test de hipótesis, y más!

  • Created by Elisa Cabana Garceran del Vall
  • Last updated 4/2019
  •  Spanish
  •  Spanish [Auto-generated]
  • 7.5 hours on-demand video
  • 17 articles
  • 22 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion

What you'll learn

  • Serás capaz de entender todos los conceptos y su estrecha relación entre sí.
  • Conseguirás realizar los ejercicios tipo test y prácticos con mucha más soltura.
  • Tendrás acceso a la explicación detallada de los métodos.
  • Verás ejercicios de ejemplo de cada tema, resueltos con tableta gráfica Wacom.
  • Tendrás disponibles los materiales complementarios con el resumen de propiedades utilizadas y con todas las fórmulas.
  • Podrás obtener un certificado válido y reconocido.

Preview This Course - GET COUPON CODE

Mathematics for Computer Games Development using Unity

games_mathematics
Mathematics for Computer Games Development using Unity, A Beginner's Guide to Essential Mathematics, Data Structures and Algorithms used in Game Programming applied in Unity

  • BESTSELLER
  • Created by Penny de Byl, Penny @Holistic3D.com
  • Last updated 4/2019
  •  English
  •  English [Auto-generated]
  • 15 hours on-demand video
  • 6 articles
  • 26 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion

What you'll learn

  • How to use bitwise operations to optimise processing and storage in games.
  • Everything there is to know about vector mathematics and how to navigate in 2D and 3D space.
  • The principles and practice behind collision detection with lines, line segments and ray casting.
  • The beauty of affine transformations and the fundamentals in transforming game objects.
  • What a quaternion is and how it is used to rotate game objects.
  • How to build a mathematics library in C# from scratch.

Preview This Course - GET COUPON CODE

Number Theory

Number Theory
Coupon Online Courses - Number Theory, Explore, Learn and Master Fundamental Topics in Number Theory

  • BESTSELLER
  • Created by Miran Fattah
  •  English
  •  English [Auto-generated]
  • 8.5 hours on-demand video
  • 2 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion

Preview This Course - GET COUPON CODE

What you'll learn

  • Have a thorough understanding of Number Theory.
  • Know different Numbers, Number Sets, Patterns, and Properties.
  • Know different Number Bases like Binary and Hexadecimal Base and how to do Arithmetics (+, -, x, ÷) in those bases.
  • Master Factorials, Double Factorials, Factorions, and many other related topics.
  • Master Divisibility, Divisibility Rules, Euclidean Division Theorem, and many other topics.
  • Learn Primes, Prime Powers, Factorial Primes, and Euclid's First Theorem.
  • Know what Fundamental Theorem of Arithmetic is.
  • Master Modular Arithmetics.
  • Learn about Finite, Infinite, and Periodic Continued Fractions.
  • Explore Public Key Cryptography, Diffie-Hellman Protocol, and RSA Encryption.

Description
Welcome to a course on Number Theory, better called “Higher Arithmetics” or “Queen of Mathematics”. This course will guide you and enable you to master fundamental topics in Number Theory.

Number theory is the study of patterns, relationships and properties of numbers. Studying numbers is a part theoretical and a part experimental, as mathematicians seek to discover fascinating and unexpected mathematical relationships and properties. In this course, you will explore some of those fascinating mathematical relationships and properties and you will learn essential topics that are in the heart of Mathematics, Computer Science and many other disciplines.




How is the course delivered?

I know visually seeing a problem getting solved is the easiest and the most direct way for a student to learn so I designed the course keeping this in mind. The materials are delivered mostly through videos to make complex subject easy to comprehend. More details on certain lessons are delivered through text files to provide more explanation or examples. The course is taught in plain English, away from cloudy, complicated mathematical jargons and that is to help the student learn the material rather than getting stuck with fancy words.



How can I learn better?

There are quizzes after each section so you can test your knowledge and see how much of the material has sank in. I suggest you go through each lesson several times to better understand the content.

Who this course is for:

  • Mathematics Computer Science, and IT Students
  • Anyone interested in understanding the fundamentals of Number Theory, aka, Queen of Mathematics.