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UNIT-3



                                                                              MATHS FOR AI


                                                               (STATISTICS & PROBABILITY)










                 Mathematics is crucial to Artificial Intelligence (AI) because it provides the theoretical foundation and practical
                 tools for developing, assessing, and optimising AI systems. It is the backbone of AI algorithms and models,
                 empowering machines to process, analyse, and interpret vast amounts of data.
                 In general, Mathematics  guarantees that AI models are precise, effective, and able to resolve challenging issues.

                         How are Math and AI Related?


                 Mathematics and AI are interconnected fields, with Mathematics supplying the theoretical foundations for many
                 AI algorithms. Patterns are repeating designs or sequences that can be observed in numbers, shapes, images,
                 languages, or objects in our surroundings. They follow a specific order or arrangement, making them easily
                 recognisable. Mathematics aids in the study of these patterns. These patterns allow you to solve puzzles. They
                 help identify an order or arrangement in lists of images or numbers. They are present everywhere around us.

                 Patterns in Numbers
                 Number patterns, often simply referred to as patterns, are sets of numbers that follow a specific order or rule.
                 There are various types of number patterns, including Fibonacci, geometric, algebraic, and arithmetic patterns.
                 Some tricks are given below for finding the patterns in numbers:

                    • Number Sequences: Look for a sequence where each number is related to the one before it in a specific way.
                   This could be:
                   ✶  Adding a constant value (e.g., 1, 4, 7, 10... +3 each time)
                   ✶  Multiplying by a constant value (e.g., 2, 4, 8, 16... x2 each time)

                   ✶  Following a formula (e.g., 2n + 1: 3, 5, 7, 9...)
                    • Series: Analyse a series of numbers to identify the underlying rule for example square series, cube series, etc.
                    • Even or Odd: Is the sequence made of even numbers (2, 4, 6...) or odd numbers (1, 3, 5...)?
                    • Prime or Composite: Are the numbers prime (only divisible by 1 and itself) or composite (divisible by more
                   than two numbers)?
                    • Fibonacci Sequence: This famous sequence starts with 0 and 1, and each subsequent number is the sum of the
                   two preceding numbers (0, 1, 1, 2, 3, 5, 8...).


                 Patterns in Images
                 Patterns in images refer to recurring visual elements or structures that can be
                 recognised and analysed within the context of an image. These patterns can
                 be  detected  and  utilised  for  various  purposes,  including  image  recognition,
                 classification, compression, and enhancement.
                    • Repeating shapes: Look for shapes that appear multiple times in the image.


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