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104 Number Theory Problems: From The Training O...


"In short, this book is a very valuable tool for any student/coach interested in preparing for mathematics competitions, especially the International Mathematical Olympiad. College students participating in the Putnam competition might also find quite a few interesting problems. Moreover, any course in number theory could be supplemented with this book and could use some of the references included. Even research mathematicians working in number theory will find this book of value in their pursuits." -MAA Online




104 number theory problems: from the training o...


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I know it is a very general question, but i'm not sure how to get started and improve number theory related skills related to ACM ICPC and other programming competitions.Any good way or book recommendations ?


For the ACM you should probably focus on their problem sets and could also look into problems from discrete mathematics. I really don't think they ask questions that rely on a graduate level understanding of number theory so reading books could be overkill for your purposes and would only confuse you if you rush it. It should take several weeks to read several chapters in a good number theory book - assuming you're not too busy (but you're in cs, right?).


Some branches of number theory may only deal with a certain subset of the real numbers, such as integers, positive numbers, natural numbers, rational numbers, etc. Some algebraic topics such as Diophantine equations as well as some theorems concerning integer manipulation (like the Chicken McNugget Theorem ) are sometimes considered number theory.


In actual programming teaching, teachers often focus on the results of problem-solving and ignore the changes in the entire thinking process of learners in solving and analyzing problems. The works or assignments created by learners become the only yardstick for judging their CT level. This kind of training model cannot improve the thinking ability of students in a real sense [3]. Scratch programming can effectively improve students' CT ability. It can be used in many aspects of teaching, such as designing animations, designing games, and solving math problems [4]. Exploring the classroom teaching implementation strategy based on scratch graphical programming in line with the current curriculum has become the top priority of information technology teaching [5]. Jiang and Li (2021) designed a scratch course aimed at improving the CT of middle school students in the teaching practice research. The result of the analysis indicated that scratch teaching improves the CT of middle school students to a certain extent [6]. Chung and Shamir (2020) studied the scratch graphical programming tool combined with the Machine Learning for Kids project to form an AI algorithm. It was applied to youth AI education for effect verification [7]. Riera et al. (2019) used the hardware logic of the perception based on the scratch teaching platform and control module as a supplement to the scratch language software logic. They also built an intelligent hardware learning system that integrates perception, processing, control, and virtual scenes [8]. The research literature suggests that CT training is mainly focused on primary and secondary schools and high schools, and there are relatively few studies in higher education. Most of the students in college have not been exposed to programming before, so the research on the cultivation of CT in college students is particularly important [9]. How to effectively cultivate CT and innovate the teaching model of CT is an important issue for college educators. The deep learning (DL) model advocates for learners to actively transfer their knowledge and apply it to solve complex problems in reality, which helps to improve learners' own critical thinking and the construction of new knowledge [10]. The learning methods are diverse, focusing on the transfer and application of knowledge, and the DL evaluation model satisfies the active and comprehensive development of learners at various aspects and levels. It transforms the actual ability of programming into the training of programming thinking, starting from scientific literacy and comprehensively inspecting students' knowledge and learning ability [11].


The DL neural network model in Figure 5 uses unsupervised learning from the input layer to the output layer. In other words, the training starts from the input layer and goes up layer by layer. The parameters of each layer are trained layer by layer without calibration data. This training can be regarded as an unsupervised training process.


Beauty is examined from an interdisciplinary perspective, taking intoaccount insights from mathematics, physics, engineering, neuroscience,and psychology, as well as philosophy, art history, and theology.Technical topics include information theory, quantum computing, fractalgeometry, complex systems, cellular automata, Boolean networks, and settheory. Prerequisite: AMTH 106 (or equivalent). Familiarity with basicconcepts in probability theory is expected, as is some experience withMATLAB. Co-requisite: ELEN 161L. (4 units)


N2 - The article highlights the problem of effective education of adults receiving the second graduate degree in Pedagogy. The importance of this problem is related to the specifics of the formation of the contingent of part-time students majoring in 013 Primary education, which is heterogeneous in age, basic education, and professional activity. The study used the method of questionnaires, interviews, observation of the educational process, methods of quantitative mathematical analysis of data processing. The normative-legal base in the context of the research is analyzed; the comparative analysis of the system of teacher training in a number of European countries is carried out. It was found that in the process of professional training of primary school teachers in the second graduate degree should take into account the following factors: age of students, their needs, social status, the availability of main education, and work due to the specialty. This determines the selection of methods and techniques of teaching, technologies that provide quality practical training, taking into account their professional and life experience, intrinsic motivation and a strong desire for self-realization. The study identified the most important principles of andragogy, which should be based on professional training of students receiving second graduate degree in pedagogic, specifically: priorities of self-study, organization of group work, use of professional experience as a source of new knowledge, relevance of knowledge and experience, self-motivation. This made it possible to identify the priority forms of organization of the educational process, to provide a practical component of the formation of subject and methodological competencies of the modern primary school teacher.


AB - The article highlights the problem of effective education of adults receiving the second graduate degree in Pedagogy. The importance of this problem is related to the specifics of the formation of the contingent of part-time students majoring in 013 Primary education, which is heterogeneous in age, basic education, and professional activity. The study used the method of questionnaires, interviews, observation of the educational process, methods of quantitative mathematical analysis of data processing. The normative-legal base in the context of the research is analyzed; the comparative analysis of the system of teacher training in a number of European countries is carried out. It was found that in the process of professional training of primary school teachers in the second graduate degree should take into account the following factors: age of students, their needs, social status, the availability of main education, and work due to the specialty. This determines the selection of methods and techniques of teaching, technologies that provide quality practical training, taking into account their professional and life experience, intrinsic motivation and a strong desire for self-realization. The study identified the most important principles of andragogy, which should be based on professional training of students receiving second graduate degree in pedagogic, specifically: priorities of self-study, organization of group work, use of professional experience as a source of new knowledge, relevance of knowledge and experience, self-motivation. This made it possible to identify the priority forms of organization of the educational process, to provide a practical component of the formation of subject and methodological competencies of the modern primary school teacher. 041b061a72


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