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COMP857 – Optimization, School of Computer Science & Informatics, University of Liverpool

From 41 $ /h

A comprehensive course in Linear Programming and Linear Optimization, based on the renowned reference:

Bertsimas, D., & Tsitsiklis, J. N. (1997). Introduction to Linear Optimization. Athena Scientific.

The course covers the first five chapters in their entirety, forming the foundation upon which everything that follows in mathematical improvement is built. The concepts are explained in clear Arabic with step-by-step solved examples, illustrations, and practice exercises.

The five lectures:

Lecture 1 — Introduction to Linear Optimization:

What is optimization? And why do we need it?

Variables, decisions, functions, and constraints

The general formula for linear programming

Standard Form

Reducing any issue to the standard formula

Piecewise Linear Convex Functions

Graphing and solution

Fundamentals of Linear Algebra

Analysis of algorithms and number of operations

Lecture 2 — Linear Programming Basics (LP Basics):

Practical examples: food issues, production, scheduling, networks, pattern classification

Converting problems to standard format

Remove free variables

Slack and Surplus variables

convex and concave functions

Absolute values in objective functions

Graphical solution in 2D and 3D

The five possible solutions

Lecture 3 — Geometry of Linear Programming (LP):

Polyhedron and Polytope

Hyperplanes & Halfspaces

Extreme Points

Vertices

Basic Feasible Solutions

Active Constraints

Degeneration

The presence of extreme points

Visual examples in 2D and 3D

Lecture 4 — The Simplex Method:

Optimality Conditions

Reduced Costs

Development of the Simplex algorithm

Simplex Tableau

Pivoting

The Revised Simplex Method

Cycling and how to avoid it

Bland's Rule

Finding a basic, possible, initial solution

Two-Phase Simplex Method

Big-M Method

Mathematical aptitude and average behavior

Klee-Minty cube

Lecture 5 — Duality Theory:

The original (Primal) and dual problem

The relationship between variables and constraints

Weak Duality Theory

Strong Duality Theory

Conditions for Complementary Slackness

Dual variables as marginal costs

Shadow Prices

Dual Simplex Method

Geometric interpretation of duality

Applications in Economics and Finance

Advantages:

🎯 Explanation based on an accredited academic reference

📐 Illustrations for each geometric concept

🧮 Solved examples with numbers

💻 Examples in Python using gurobipy

📊 Comparison tables between different formulas

🔗 Linking theory to practical applications

📝 Exercises at the end of each lecture

Extra information

Prerequisites:

Basic knowledge of linear algebra (vectors, matrices, inner product)

Basic knowledge of calculus (for convex concepts)

Basic knowledge of Python (optional, for practical examples)

Primary reference:

Bertsimas, D., & Tsitsiklis, J. N. (1997). Introduction to Linear Optimization. Athena Scientific.

Tools used:

pip install gurobipy (for practical problem solving)

Python 3.x or any programming environment

expected outcomes:
Upon completion of the course, the student will be able to:

Formulating real-world problems such as linear programming problems

Converting any problem to the standard formula

Understanding the algebraic geometry of a polyhedron

Applying the simplex method manually and programmatically

Interpretation of dual solutions and shadow prices

Using Python to solve linear optimization problems

Reading and understanding research papers in the field of improvement

the target audience:

Engineering students (electrical, industrial, mechanical)

Computer Science and Artificial Intelligence Students

Operations Research and Statistics students

Economics and Finance Students

Researchers and practitioners in the field of improvement

Location

Online from Egypt

About Me

Engineer Abdulrahman Mudarris
For Industrial Engineering and Mechanical Engineering materials at Cairo University

A teacher specializing in industrial and mechanical engineering, he has over 8 years of experience teaching engineering subjects in a simple and accessible style suitable for all levels. He is characterized by patience and cooperation, and provides continuous follow-up with students throughout the year to ensure optimal results.

Education

Bachelor of Engineering from the Faculty of Engineering, Cairo University
Teaching Assistant at the Faculty of Engineering, Cairo University, specializing in Industrial and Mechanical Engineering
I also worked as a teaching assistant at the Faculty of Engineering, Tanta University.

Experience / Qualifications

✔️ Over 8 years of continuous experience teaching engineering subjects to university students, both in Egypt and the Gulf, through direct private online lessons.

✔️ Specializes in teaching a wide range of subjects, including:

Operations Research (1 and 2)

Project Management

Production and Operations Management

Engineering Economics and Accounting

Production Planning and Supply Chains

Analysis of stresses, structures, and collapses

Engineering Materials and Materials Testing

And other industrial engineering materials and design and production engineering materials

Age

Children (7-12 years old)

Teenagers (13-17 years old)

Adults (18-64 years old)

Seniors (65+ years old)

Student level

Beginner

Intermediate

Advanced

Duration

45 minutes

60 minutes

90 minutes

120 minutes

The class is taught in

English

Arabic

Skills

Tutoring

Math

Computer science

Reviews

Availability of a typical week

(GMT -04:00)

New York

Online via webcam

Mon

Tue

Wed

Thu

Fri

Sat

Sun

00-04

04-08

08-12

12-16

16-20

20-24

شرح دروس خصوصيه في مادة إدارة الإنتاج والعمليات Production and Operations Management

42 $ /h

• I specialize in teaching Production and Operations Management for engineering and business students. My lessons focus on helping students understand core concepts, solve related problems, and prepare for exams. I stay in contact with students throughout the semester and provide recorded explanatory lectures along with handouts to support learning and revision.

• This course is designed for engineering and management students who want to understand how companies design and manage production systems. We will cover the following key topics:

Introduction to Operations Management

Demand Forecasting

Product and Process Design

Capacity Planning

Facility Location

Facility Layout

Inventory Management

Production Planning and Scheduling

Quality Management

Supply Chain Management

بحوث العمليات 1 Operations Research 1 for Engineering and Management Students

42 $ /h

I specialize in teaching Operations Research 1 for engineering and management students. My lessons focus on helping students understand core concepts, solve related problems, and prepare for exams. I stay in contact with students throughout the semester and provide recorded explanatory lectures along with handouts to support learning and revision.

This course is designed for engineering and management students who want to learn how to apply mathematical and analytical techniques to make better decisions in production, operations, and business systems.

We will cover key topics such as:

Introduction to Operations Research

Linear Programming

Simplex Method

Transportation and Assignment Problems

Integer Programming

Network Models (Shortest Path, Max Flow, Min Cost Flow)

Project Management Techniques (PERT/CPM)

Students will learn how to formulate real-world problems mathematically, analyze them using OR techniques, and interpret the results to make effective operational decisions.

Jonathan

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My name is Jonathan. I am a young teacher with already 15 years of experience in the field of academic support for primary and secondary school children up to rhetoric.

I also provide individual monitoring for your work method, more particularly in terms of understanding the instructions and the work schedule. If you need a helping hand, I'm here to listen.

Benoit

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I am a qualified and experienced mathematics tutor. Graduated from the Free University of Brussels in 2011, I started my career by teaching remedial courses in different schools in Brussels. I then specialized in individual academic support by following educational training at the Harvard Graduate School of Education. I have been giving private mathematics lessons daily for over ten years.

The students who follow my private lessons benefit from personalized support. The first session is devoted to an in-depth assessment of the student's mathematical knowledge. The objective is to detect its weak points and understand their origin in order to adapt my courses to its needs. I develop a tailor-made remediation program for each of my students aimed at filling each of their gaps. Over the course of the sessions, the student builds a solid foundation for learning and regains self-confidence. At the same time, I help him acquire a work methodology that allows him to gradually become autonomous in his studies.

I have a thorough knowledge of the mathematics curriculum for middle and high school (from 6th to 12th grade). I am also qualified to support students in preparing for international exams such as the SAT, the OMPT, and the International Baccalaureate (IB) in all its variations: Analysis and Approaches (AA SL/HL) and Applications and Interpretation (AI SL/HL).

Throughout my years of training, I studied and developed numerous techniques that facilitate learning mathematics. The strength of my teaching approach lies in my ability to explain, in simple terms, anything a student finds complicated. I am passionate about this profession because it offers me the opportunity to guide struggling students toward success. It is a true pleasure to see them progress and rediscover their connection with the fascinating world of mathematics.

I offer private tutoring in Paris (at the student's home) or remotely (online). My online lessons take place on an interactive whiteboard. This whiteboard is specifically designed to facilitate student/teacher interaction online. Thanks to this teaching tool, my online lessons are just as effective as in-person lessons. The student only needs an internet connection and a computer, tablet, or smartphone to participate.

Raef

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Experienced and qualified teacher gives private lessons at home or online using a very modernized method of Mathematics - Analysis - Matrices - Statistics - Algebra - Physics - Chemistry - Biology and Geology from the French or International or European program (in English) to students of Terminale, 1ère, Seconde, Brevet, Concours and university preparatory classes of 1st year university.
You can contact me for details.
Specific program for CNED students or those of International School in english.
My students' results are All with VERY GOOD, GOOD AND EXCELLENT grades.
Feel free to contact me for more information; a response is guaranteed within minutes to a maximum of 12 hours.

Carolina

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Firstly, this lesson ensures that you as a student feel at ease! We will first get to know each other a little bit, and then you can tell me what you expect/want in a lesson, or what you specifically need. Step by step, I will ensure you, that you as a student, will learn the Dutch language. You will come to me for different reasons, for example for an integration exam, or because you live temporarily as an expat in the Netherlands and want to learn the language, others enjoy it as a hobby and others come to the Netherlands for love... There are so many reasons! My lessons are tailored to your wishes, you indicate what you want, and I will help you with it, which will make you feel more at ease. From teenage to adult students, from beginner to advanced and in between, I enjoy teaching my classes all over the world! Curious?! Then I hope to see you in my class! Greetings Carolina

Amin

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Python is the most in-demand programming language in the world right now — and one of the easiest to learn with the right guidance.
Whether you've never written a line of code or you're a student who needs to pass a programming course, this is a practical, no-fluff introduction that gets you writing real code from session one.
What we can cover depending on your goals:

Python fundamentals: variables, loops, functions, data structures
- Object-oriented programming (OOP)
- Data manipulation with pandas and NumPy
- Introduction to machine learning with scikit-learn
- Database management with SQL
- C and Java upon request
- MATLAB and R available for engineering/science students

Why learn with me?
I'm not a student teaching on the side — I'm a professional engineer who uses Python daily for data analysis, modeling, and automation. I know exactly which concepts matter in the real world and which ones you can skip for now.
Sessions are 100% personalized: I adapt the pace, the examples, and the exercises to your background and your goal — whether that's passing your university exam, building a project, or landing a job.

Arno

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Since the Gymnasium I give tutoring Mathematics, Physics, Chemistry, Latin and language courses Latin languages Portuguese Spanish French and Italian from basic or beginner level to Gymnasium level. For primary school students also arithmetic for example with fractions and percentages and all other modules. Also Dutch grammar and spelling.

Lucía

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Hi! Do you love Korean culture, food, music, or dramas? Would you like to learn Korean but don't know where to start? Are you planning a trip to Korea? I'm a Korean teacher with international academic training and several years of experience teaching students of all levels and with diverse goals. I've been teaching online Korean and Spanish classes for over five years. If you're afraid to speak because you feel you don't have a solid foundation or you're intimidated by all the cartoons, I completely understand: I've been there too! I'll help you take your first steps in the language with confidence and without fear of making mistakes. 😊

🎓 About me
- PhD in linguistics applied to language teaching
- Master's degree in International Education and Bilingualism.
- Graduated in East Asian Studies (specializing in Korea).
- Korean language and literature studies at Seoul University.
- Official language teaching qualification.
- Korean family, which allows me to teach you the language along with the real culture and natural expressions.
- More than 2 years living in Korea (university exchange and intensive TOPIK 3–5 language program).

👩‍🏫 Teaching experience
- Language teacher with international experience.
- Years teaching Korean to beginner students and East Asian degree students
- Clear, communicative methodology adapted to your pace.

📚 My classes
✔ Customized according to your objectives (TOPIK, conversation, travel, culture, leisure).
✔ Simple and structured explanations
✔ Material included.
✔ Friendly and motivating environment.
✔ Continuous monitoring and feedback.

💻 Modality
Online or in-person classes.

⭐ Ideal for you if you want:

Start from scratch without stress.
Improve your speaking and real comprehension.
Prepare for TOPIKE I
Understanding Korean culture in addition to the language.

📩 Contact me and we'll design your personalized learning plan. Learning Korean can be fun, effective, and motivating!

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I am happy to help you learn the French language: 📚written or 🎤🎧oral or both. It depends on your needs.

I follow the institut Français programmes to design my course.
Through videos, audios, images, texts, songs, stories... learners will learn how to listen, speak, read, and write in French.

You will be comfortable and motivated. There will be no stress or routine. I am patient and a good listener.

If you want to improve your French skills, or you have an exam or homework, contact me💐 🏵️

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Welcome to my Maths, Physics and Science tutoring class, crafted especially for young minds preparing for IB MYP, IGCSE, and GCSE exams. As a passionate learner and dedicated tutor, I am committed to helping students not only comprehend but also develop a love for these captivating subjects. Here's what you can anticipate from my tutoring sessions

Personalised Learning: Every learner is unique, and I believe in tailoring my teaching methods to suit each student's individual needs. I don't judge; instead, I concentrate on understanding their strengths and areas for improvement to create a supportive and encouraging learning environment.

Concept Breakdown: I dissect complex topics into simpler, more manageable parts, making it easier for students to grasp challenging concepts and build a strong foundation in Physics and Science.

Student-Centred Approach: I enjoy teaching students and continually strive to ignite their curiosity and passion for learning. I aim to make each lesson engaging and enjoyable, helping students recognise the real-world applications of what they learn.

Shared Strategies: As a student who has successfully qualified for the Engineering Entrance exam test and is currently studying abroad on a fully funded scholarship, I bring my own learning strategies and study techniques to the table. These proven methods will help students achieve their academic goals.

Continuous Improvement: I am always learning and growing, just like my students. This continuous improvement mindset, which I actively promote, inspires and motivates students to strive for their best. It enables me to stay updated with the latest educational trends and techniques, ensuring that my students receive the best possible guidance.

Supportive Environment: I encourage students to ask questions, no matter how trivial they might seem. By creating a friendly and comfortable atmosphere, I ensure that students feel comfortable and open to express their doubts and curiosities, leading to a deeper understanding of the subjects.

Khalid

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Are you looking for comprehensive and personalized tutoring to boost your skills and confidence in mathematics, excel in the IELTS exam, or prepare for the OMPT-D test? Look no further! I offer specialized one-on-one and group tutoring tailored to meet the individual needs of students in three key areas:

Middle School Mathematics:
Master essential math concepts, including algebra, geometry, fractions, decimals, percentages, and more.
Develop problem-solving strategies, logical thinking, and a strong foundation in mathematics.
Tailored lessons designed to match your pace and help you succeed in school assessments and standardized tests.
IELTS Exam Preparation:

Focused preparation for all four sections of the IELTS:
Listening, Reading, Writing, and Speaking.
Practice with real IELTS materials, timed mock tests, and personalized feedback on essay writing and speaking responses.
Learn effective strategies for achieving your desired band score, whether it's for academic purposes or immigration.

OMPT-D Prep (Online Mathematics Proficiency Test):
Comprehensive preparation for the OMPT-D, focusing on calculus, algebra, and problem-solving skills.
Step-by-step explanations of complex mathematical concepts and sample test problems.
Tailored strategies to optimize your performance on this challenging university entrance exam.

Why Choose Me?

Experienced Tutor
Engaging and interactive Teaching Style
Flexible Scheduling
Personalized Feedback on weaknesses to improve

Let’s work together to achieve your academic goals and unlock your full potential!

Baia

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I teach Python specifically for finance and data applications - the kind used in economics, business analytics, and quantitative programs. This isn't a general "learn to code" course; it's built around real financial data, benchmarking, and the workflows you'll actually use in coursework or early career work.

Topics include:
Python fundamentals through a finance lens (data structures, functions, control flow).
Working with financial data and datasets.
Performance benchmarking and writing efficient code.
Applying concepts from Hilpisch's Python for Finance.

Nouhaila

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This course is designed for primary, secondary, or even university students who need support with their homework, want to better understand their lessons, or prepare for exams.

I offer personalized guidance in a friendly and supportive environment to help students:

Understand instructions and complete exercises

Review and reinforce difficult concepts

Develop effective study habits

Build confidence and become more independent

📚 I can assist with various subjects (languages, humanities, etc.) depending on the level.

💡 My goal: to ensure students never feel alone with their homework and to help them enjoy learning again.

Lessons are available in person or online, depending on your preference.
Feel free to get in touch to discuss your or your child's specific needs!

This course is aimed at primary and secondary school students, or even college students who need support to do their homework, better understand their lessons, or prepare for an exam.

I offer tailor-made assistance, in a caring and encouraging atmosphere, for:

Understanding the instructions and exercises

Review concepts not acquired

Developing effective working methods

Gain autonomy and confidence

📚 I can teach in several subjects (languages, humanities, etc.) depending on the level.

💡 My goal: that the student never feels alone when it comes to their homework, and that they rediscover the joy of learning.

Courses available in person or online, depending on your preferences.
Please do not hesitate to contact me to discuss your child's specific needs!

Reza

4.6

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I hold a PhD in Mechanical Engineering and currently work as a post-doctoral researcher in the Aerospace Engineering Faculty at TU Delft (Delft University of Technology).
Key topics that I teach for this course include:
• Calculus: Differentiation & integration, Multivariable calculus
• Linear Algebra: Matrices, vectors, systems of equations, Eigenvalues and eigenvectors
• Differential Equations: First- and second-order ODEs, Laplace transforms
• Complex Numbers: Polar form, Euler’s formula
• Vector Calculus: Gradient, divergence, curl, Line and surface integrals
• Series & Transforms: Taylor series, Fourier series

I understand that not all teachers excel in teaching Engineering and Mathematics courses and explaining their importance to students. Courses with strong mathematical backgrounds may become boring for students who lack a solid mathematical basis. To address this, I take a student-centered approach, starting from the basics to actively engage all students, including those with weaker mathematical backgrounds. I also provide practical examples to demonstrate the real-world significance of what they are learning, inspiring and fostering their interest in the subject matter.

If you have any additional questions before starting a class, please feel free to ask me. I am here to assist! :)

Mariem

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Understanding algorithms is essential for anyone pursuing computer science or programming. In this course, I provide a structured approach to learning algorithms—from fundamental concepts like sorting and searching to advanced techniques such as dynamic programming and graph theory. Whether you're preparing for exams, coding interviews, or aiming to improve your problem-solving skills, this course is designed to build strong algorithmic thinking. Through practical examples and step-by-step explanations, I help students master the logic and techniques needed to write efficient and elegant code.

Fisnik

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Are you taking a mathematics exam in the second session?
I offer intensive support to review the basics, target important chapters and practice effectively on typical exercises.

I support higher education students, particularly at university, college and Solvay/ULB, to understand important concepts, redo practical exercises and practice on typical exam exercises.

My goal is simple: to help you understand the logic behind the methods, know when to use each formula, recognize the correct reasoning in a statement and gain autonomy when facing exercises.

Subjects covered according to your program:

• Limits and continuity:
Calculation of limits, indeterminate forms, left-hand and right-hand limits, limits at infinity, horizontal, vertical and oblique asymptotes, continuity and behavior of a function.

• Derivatives and function analysis:
rules of differentiation, derivative of a composite, logarithmic derivative, increasing/decreasing, extrema, convexity/concavity, inflection points, variation tables and complete graphical representation.

• Optimization:
maximum/minimum problems, economic optimization, cost functions, revenue, profit, elasticity, choice of method and interpretation of results.

• Functions with several variables:
partial derivatives, gradient, differentials, two-variable optimization, local extrema, Hessian matrix, first-order conditions and economic interpretation according to your course.

• Constrained optimization:
Lagrange method, budget constraint, utility maximization, cost minimization, Lagrange multipliers and interpretation of results.

• Linear algebra:
vectors, matrices, matrix operations, determinants, inverse matrices, rank of a matrix, systems of linear equations, Gauss's method and solving systems.

• Sequels and series:
arithmetic and geometric sequences, limits of sequences, convergence, sums, simple series and economic or financial applications according to your program.

• Integrals:
antiderivatives, definite integrals, area under a curve, simple calculation methods, graphical interpretation and applications.

• Financial mathematics:
Simple and compound interest, capitalization, discounting, present value, future value, annuities, monthly payments, equivalent rate, effective rate, loans, repayments, NPV, IRR and basic financial applications.

• Exam preparation:
reading statements, choosing the right method, identifying the formulas to use, typical exercises, past exams, guided corrections and problem-solving methods.

Method of working :

1. We quickly identify the chapters that are causing problems;
2. I re-explain the theory with simple examples;
3. We redo the important exercises together;
4. I will show you how to recognize good reasoning in the exam;
5. We construct a clear method that can be reused independently.

I don't just provide a correction: I explain the reasoning step by step so that you are able to redo the exercises without help.

I have been giving private lessons for over 7 years in mathematics, statistics, economics, and accounting. I have also tutored first and second-year Bachelor's students at Solvay/ULB in mathematics, statistics, and microeconomics as part of a university tutoring program.

My professional experience in finance and business controlling at Deloitte has also allowed me to develop a very structured approach to numbers, analysis, financial models and problem-solving.

Courses available in French or English, online or in person in Brussels or the surrounding area.