1 00:00:09,830 --> 00:00:13,190 Everything is number. Or at least, 2 00:00:13,190 --> 00:00:16,310 it is for a Computer Scientist like you. 3 00:00:16,310 --> 00:00:20,280 In this module, we will work through numerical tools that will 4 00:00:20,280 --> 00:00:24,755 support your journey as a Computer Scientist. 5 00:00:24,755 --> 00:00:29,895 I want to invite you to think of what I mean with everything is number. 6 00:00:29,895 --> 00:00:33,050 Right down from a scale from one to 10, 7 00:00:33,050 --> 00:00:35,370 how much you agree with that statement? 8 00:00:35,370 --> 00:00:37,390 Ten is total agreement. 9 00:00:37,390 --> 00:00:40,920 It is a number. Jot down your thoughts on it, 10 00:00:40,920 --> 00:00:42,985 and write the date. 11 00:00:42,985 --> 00:00:45,280 As you progress along this module, 12 00:00:45,280 --> 00:00:48,950 revisit this question and add any new thought, 13 00:00:48,950 --> 00:00:52,910 and do join the discussion forum on this topic, 14 00:00:52,910 --> 00:00:56,475 and see what your module colleagues came up with. 15 00:00:56,475 --> 00:00:59,310 Now, my name is Sarah Santos. 16 00:00:59,310 --> 00:01:00,880 I was born in Portugal, 17 00:01:00,880 --> 00:01:02,825 and I live in London in the UK. 18 00:01:02,825 --> 00:01:06,710 I'm a mathematician with a love for arts and passion for computing. 19 00:01:06,710 --> 00:01:10,245 I love knitting socks, wrapping a present, 20 00:01:10,245 --> 00:01:14,545 mathematically respecting the wrapping paper pattern, 21 00:01:14,545 --> 00:01:17,300 and I love dancing. 22 00:01:17,300 --> 00:01:21,340 Tell us more about you in the discussion forum. 23 00:01:21,350 --> 00:01:24,240 Now, back to you on computing. 24 00:01:24,240 --> 00:01:26,224 On a day to day basis, 25 00:01:26,224 --> 00:01:32,750 you will abstract from how a computer works at the very basic machine level. 26 00:01:32,750 --> 00:01:38,830 Still, a basic understanding of the numerical foundation of how computers work, 27 00:01:38,830 --> 00:01:44,530 will help you be an effective problem solver and a creative professional. 28 00:01:44,530 --> 00:01:47,110 That's a pretty cool Computer Scientist. 29 00:01:47,110 --> 00:01:49,610 Computers compute. 30 00:01:49,610 --> 00:01:53,200 All information is computed as numbers. 31 00:01:53,200 --> 00:01:56,410 Whether you are manipulating pixels of images, 32 00:01:56,410 --> 00:02:01,580 creating websites, transforming sound, creating music, 33 00:02:01,580 --> 00:02:06,545 analyzing business data, designing VR or video games, 34 00:02:06,545 --> 00:02:11,155 you will always use tools with a mathematical base. 35 00:02:11,155 --> 00:02:13,730 I love mathematics, and I particularly, 36 00:02:13,730 --> 00:02:17,900 enjoy witnessing people connecting with their inner mathematician. 37 00:02:17,900 --> 00:02:22,440 A common ground we have as humans is a want for patterns. 38 00:02:22,440 --> 00:02:26,610 The number sense and a need to express thoughts numerically, 39 00:02:26,610 --> 00:02:29,605 is part of this knack for patterns. 40 00:02:29,605 --> 00:02:32,520 We, humans are pattern searchers, 41 00:02:32,520 --> 00:02:37,105 and mathematics is the ultimate expression of our conquest of patterns. 42 00:02:37,105 --> 00:02:40,250 The word mathematics comes from "mathema," that relates to 43 00:02:40,250 --> 00:02:43,725 gaining knowledge to really knowing something. 44 00:02:43,725 --> 00:02:50,900 Patterns, rhythm, beauty, and the pleasure that comes from those are a very human thing. 45 00:02:50,900 --> 00:02:53,615 People specialize on how they deal with patterns. 46 00:02:53,615 --> 00:02:54,850 Paint it, dance it, 47 00:02:54,850 --> 00:02:56,130 sing it, drum it, 48 00:02:56,130 --> 00:02:59,390 feel them cause patterns in others via words, code, 49 00:02:59,390 --> 00:03:04,465 laughter, medicine, others, even without a physical context. 50 00:03:04,465 --> 00:03:07,175 Being a mathematician, observing patterns, 51 00:03:07,175 --> 00:03:09,365 seeking the rule behind them, 52 00:03:09,365 --> 00:03:11,650 being able to know things for sure, 53 00:03:11,650 --> 00:03:13,930 proving that the rule works. 54 00:03:13,930 --> 00:03:17,000 Also, being baffled by the mysteries of patterns, 55 00:03:17,000 --> 00:03:18,925 is all part of being human. 56 00:03:18,925 --> 00:03:23,585 It is the process of studying patterns that we nowadays call mathematics. 57 00:03:23,585 --> 00:03:27,190 But deep down, we are all mathematicians. 58 00:03:27,190 --> 00:03:31,505 Some of the mathematics we cover here may be familiar to you. 59 00:03:31,505 --> 00:03:34,450 Other parts may seem outlandish, 60 00:03:34,450 --> 00:03:37,750 but we keep it all linked to computing situations, 61 00:03:37,750 --> 00:03:40,600 and we invite you to always place the maths we 62 00:03:40,600 --> 00:03:44,600 learn in the context of a theme or a problem in computing. 63 00:03:44,600 --> 00:03:47,605 We will support you on that journey, too. 64 00:03:47,605 --> 00:03:50,660 But, what have I got in store for you? 65 00:03:50,660 --> 00:03:55,035 This module is designed as a walking and climbing journey. 66 00:03:55,035 --> 00:03:56,490 We're in it together, 67 00:03:56,490 --> 00:03:58,510 and I have prepared a way. 68 00:03:58,510 --> 00:04:04,840 You are going along the same path with enough room for you to do your own footsteps, 69 00:04:04,840 --> 00:04:06,785 but you are to do the walking, 70 00:04:06,785 --> 00:04:10,585 and you all can talk along the way. 71 00:04:10,585 --> 00:04:13,370 I'll point out some beautiful bits on the landscape. 72 00:04:13,370 --> 00:04:16,560 You will have options to go off the track sometimes, 73 00:04:16,560 --> 00:04:18,460 but with insight of the journey, 74 00:04:18,460 --> 00:04:19,960 you can stop or have a break, 75 00:04:19,960 --> 00:04:21,190 and then race back in. 76 00:04:21,190 --> 00:04:22,990 You can also talk along the way, 77 00:04:22,990 --> 00:04:25,880 and I hope you also point out to all of 78 00:04:25,880 --> 00:04:29,880 us when you find a new flower tree or special rock along the way. 79 00:04:29,880 --> 00:04:36,619 The videos that contain examples were made thinking about you stopping 80 00:04:36,619 --> 00:04:43,080 the video and working through the example yourself with good old-fashioned pen and paper, 81 00:04:43,080 --> 00:04:45,355 before you check against my results. 82 00:04:45,355 --> 00:04:49,055 Don't be tricked by the need to be right all the time. 83 00:04:49,055 --> 00:04:54,690 The surprise of being wrong and learning from it is a very valuable experience. 84 00:04:54,690 --> 00:04:56,995 So, enjoy it and learn. 85 00:04:56,995 --> 00:05:00,550 Sometimes, you'll be asked to read something in advance, 86 00:05:00,550 --> 00:05:01,590 or think of a problem, 87 00:05:01,590 --> 00:05:03,670 or revise a topic before a lecture. 88 00:05:03,670 --> 00:05:09,545 Do it, and bring your own notes and thoughts, questions with you. 89 00:05:09,545 --> 00:05:14,180 After each video, do attempt the formative quizzes as soon 90 00:05:14,180 --> 00:05:16,280 as possible to understand if you need to revisit 91 00:05:16,280 --> 00:05:18,955 the videos or if you can progress to the next. 92 00:05:18,955 --> 00:05:23,100 The point of the formative quizzes is for you to get feedback on your learning, 93 00:05:23,100 --> 00:05:24,710 so do attempt early on, 94 00:05:24,710 --> 00:05:26,265 and as often as you need. 95 00:05:26,265 --> 00:05:29,635 Embrace the difficulties as learning moments, 96 00:05:29,635 --> 00:05:33,120 and share your questions and thoughts in the discussion forum. 97 00:05:33,120 --> 00:05:35,735 We want you to succeed. 98 00:05:35,735 --> 00:05:40,295 There will be tasks with problem solving elements and some peer reviews. 99 00:05:40,295 --> 00:05:43,610 You are encouraged to discuss some elements of these tasks in 100 00:05:43,610 --> 00:05:47,200 the forum to make sure you understand the assignment. 101 00:05:47,200 --> 00:05:50,280 There will be at least one summative quiz per topic, 102 00:05:50,280 --> 00:05:53,350 but they contain questions that require you haven't 103 00:05:53,350 --> 00:05:58,115 completed previous tasks in order to be able to answer. 104 00:05:58,115 --> 00:06:02,165 We will look at binary and other number basis, 105 00:06:02,165 --> 00:06:06,510 sequences, series, and graphs of functions. 106 00:06:06,510 --> 00:06:09,225 Come along with us in this journey, 107 00:06:09,225 --> 00:06:12,080 and enjoy the module.