Introduction
- Introduction
- Base Formation
- Basic Properties of Congruency
- Divisibility Techniques
- Some Numerical Problems
- Advanced Levels Problems and Solutions
- Some Important Theorems and their Applications
- Chineses Remainder Theorem
- Conclusion
What you'll learn
- Advanced concepts of modular arithmetic, including modular inverses and extended Euclidean algorithm.
- Applications of modular arithmetic in cryptography and error detection.
- Chinese Remainder Theorem and its use in solving systems of linear congruences.
- Fermat's Little Theorem and Euler's Totient Function for advanced number theory applications.
- Advanced techniques for solving Diophantine equations using modular arithmetic.
- In-depth exploration of modular exponentiation and its significance in computer science and cryptography.
Description
Embark on a captivating intellectual journey as you enroll in our "Modular Arithmetic: Advanced Level of Number Theory" course. This comprehensive exploration goes beyond the basics, immersing you in the fascinating intricacies of modular arithmetic. Uncover the secrets of modular inverses, a crucial component in the toolkit of advanced mathematicians, and witness their applications in cutting-edge fields such as cryptography and error detection.
The Chinese Remainder Theorem takes center stage, offering a powerful method for solving systems of linear congruences. As you delve into the realm of number theory, discover the elegance of Fermat's Little Theorem and the versatility of Euler's Totient Function, both indispensable in advanced mathematical applications. Navigate through the maze of Diophantine equations using sophisticated techniques, gaining a nuanced understanding that sets you apart in the world of advanced mathematics.
Our course places a spotlight on modular exponentiation, showcasing its vital role in computer science and cryptography. Tailored for mathematics enthusiasts hungry for intellectual challenges, advanced students seeking to expand their knowledge, and professionals aiming to apply these concepts in practical scenarios, this course promises a comprehensive and insightful exploration. Elevate your comprehension of abstract algebra, gaining tools that can be wielded across various disciplines.
Enroll now and unlock the doors to a profound understanding of advanced modular arithmetic. Embark on a journey of mathematical discovery and mastery that will reshape your perspective on number theory and its real-world applications. Your intellectual odyssey awaits – seize the opportunity to elevate your mathematical prowess and broaden your horizons.
The University of Sheffield
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About the instructors
- 3.92 Calificación
- 5803 Estudiantes
- 20 Cursos
Sourav Das
Google certified Trainer, Professor, Author , Entrepreneur
12+ years experience teaching in schools, colleges, universities also in national ands international level. I have made more than 7000 videos made for online courses, 250+ study materials and books on Amazon.
I have worked with students who were complete beginners, as well as those who were facing challenges in mastering advanced topics.
I completely understand the initial struggle in decoding the concepts and formulas. I am thoroughly proficient in explaining difficult and hard to understand topics in a lucid, useful , quick and enjoying manner. You will find ample examples and examination level explanations in my videos , notes , materials and special mock tests. My classes will be your way to get rid of the intense mug up sessions and will take you to the real fun of studying.
Just like our faces we are all different in understanding concepts , ideas , concepts so in my classes too the same approach is being taken so that you always come out with flying colours and greats grades of marks . With my personal innovative teaching methods I will be making your journey towards goals a very smooth run.
Let the journey begin…
Student feedback
4.5
Course Rating
Reviews
Saheli
15-02-2024
I found this course incredibly helpful in clarifying complex concepts, particularly in the realm of Modular Arithmetic within advanced Number Theory. The instructor's approach was clear and concise, making difficult topics much more accessible. By the end of the course, I had a solid understanding of the material, which was reflected in my ability to confidently apply it.