Summary of Mod-01 Lec-01 Introduction, Why and how we need computers

00:00:00 - 00:45:00

This YouTube video introduces the concept of computers and how they are used in mathematics. The presenter explains how equations can be solved using methods such as bisection and Newton's Method. He also mentions how computer representations of functions can be helpful in solving such equations. The video ends with a discussion of why it is important to use computers in these situations.

• 00:00:00 The video describes how to find a solution to an equation in algebraic or algebraic-linear equation systems on a computer. If the solution is not a number, then it is not always a number and may require the use of complex numbers.
• 00:05:00 In this video, the presenter introduces computers and how they are used in mathematics. He goes on to explain how equations such as the one in the title can be solved using methods such as bisection and Newton's Method. He also mentions how computer representations of functions can be helpful in solving such equations. The presenter ends the video by talking about why it is important to use computers in these situations.
• 00:10:00 The video introduces the mod-01 Lec-01, which is a computer that can solve equations that cannot be solved by hand. The mod-01 Lec-01 has a finite sum and a solution can be found by systematically trying different solutions until one is found. The second reason why the computer is necessary is to automate the process of solving equations.
• 00:15:00 In this video, the presenter describes how computers represent numbers and symbols. Binary digits (bits) can take on two values, one representing a one and the other representing a zero. Four bits can represent sixteen symbols, which can be used to represent any number from zero to nine. With eight bits, computers can represent up to 2^16, or forty-eight, symbols.
• 00:20:00 The video introduces the concept of computers and how they work. It explains that a computer uses a four bit representation of numbers, which allows it to do math using only four symbols. It then goes on to show how to build a four function calculator using these symbols. However, this is not the only way computers can represent numbers. It also discusses how to use fixed point arithmetic, which allows for more complex calculations.
• 00:25:00 Fixed point arithmetic is faster than integer arithmetic, but it can lose significant digits when numbers are subtracted. Recurring fractions have a finite representation, while non-recurring fractions have a recurring representation.
• 00:30:00 Computers need to use fixed-point arithmetic because decimal representation is not accurate enough. Floating point representations allow for a greater range of numbers.
• 00:35:00 This YouTube video introduces the concept of computers and floating point arithmetic. It explains that computers use a standard to represent floating point numbers, and that binary numbers have an advantage because they can either be one or zero. The video finishes by providing a brief explanation of how to shift a number in binary.
• 00:40:00 In this video, the presenter discusses how computers use a floating point representation. He explains that the smallest positive number such that one plus epsilon equals one is called the epsilon. He then writes a pseudo code to find this number.
• 00:45:00 In this video, the presenter explains how computers are necessary to solve differential equations, and how to represent functions and differential equations on a computer.