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MINISTRY OF EDUCATION AND TRAINING THE VIETNAM NATIONAL INSTITUTE OF EDUCATIONAL SCIENCES - - NGUYEN VAN DAI TEACHING PROBABILITY AND AND STATISTICS FOR STUDENTS ON TECHNICAL RECONNAISSANCE AT MILITARY SCIENCE ACADEMY IN THE DIRECTION OF INTEGRATION WITH INFORMATION THEORY Specialty: Mathematics Theory and Methods of Teaching Code: 14 01 11 SUMMARY OF DOCTORAL THESIS ON EDUCATION HANOI - 2020 The research was finished at: THE VIETNAM NATIONAL INSTITUTE OF EDUCATIONAL SCIENCES Full name of scientific instructors: Assoc.Prof Dr DO TIEN DAT Dr PHAN THI LUYEN Judge 1: ………………………………………… Judge 2: ………………………………………… Judge 3: ………………………………………… The thesis will be defended before the Thesis Assessment Council at Institute level, meet at the Vietnam National Institute of Educational Sciences 101 Tran Hung Dao street, Hanoi At, … hour … date … month … year 2020 Be able to search the thesis at: - National library, Ha Noi - The Vietnam National Institute of Educational Sciences library INTRODUCTION Reason for choosing the topic 1.1 Military Science Academy is responsible for training students in the fields of Military Science, Technical Reconnaissance, and foreign languages for the Army One of the top tasks of Military Science Academy right now is to train and develop the technical reconnaissance major to produce a contingent of learners, officers as well as soldiers with resilient political character, absolute loyalty to the leadership of the Party and the Army, good professional expertise and capability to solve practical problems The technical reconnaissance soldiers’ main job is to collect enemy information, decrypt information, analyze data, publish and report the results to the superior commanders To the job well, technical reconnaissance students need to be equipped with the necessary systemized knowledge and have a synchronous and scientific combination of many subjects such as knowledge of Information theory (Signal transmission theory, encryption, decryption, cryptanalysis), knowledge of equipment , mathematics, linguistics, information technology, etc In which, Probability and Statistics is one of the subjects that plays an important role in fulfilling the above requirement Probability and Statistics is the most essential tool to discover codes, but the characteristics of different coding systems have different ways of discovering, thus requiring lecturers to have appropriate teaching methods for each targeted group of learners and teach them how to statistics However, at present, the teaching and learning of Probability and Statistics at Military Science Academy still exist a number of limitations, thus, have not yet met the above mentioned objectives The teaching process has not been able to promote students' initiative and creativity and the content of Probability and Statistics knowledge has not got the connection with the knowledge of Information theory and profession reality, making the learners not fully aware of the practical meaning of the subject 1.2 Information theory (according to the training objectives at Military Science Academy includes the fields of signal transmission theory, encryption, decryption, cryptanalysis The role of Information theory is to effectively support the work of technical reconnaissance soldiers Regarding information theory in general and coding theory in particular, the Probability and Statistics theory plays a very important role as the foundation Thanks to the application of the Probability and Statistics theory, we can assess the quality of a coding system, or survey and evaluate sources before taking the next processing steps The work of discovering transmission codes is very important for technical reconnaissance forces because if the transmission code cannot be discovered, there is no data for processing, broadcasting and there is no data available for decryption Research on discovering transmission code is an important and indispensable task in technical reconnaissance Nevertheless, this is an extremely daunting job for the technical reconnaissance force in both theory and practice The work of discovering transmission codes relates to many fields such as informatics, linguistics, foreign languages, and mathematics, including the theory of engineering reconnaissance 1.3 There have been many research topics on teaching technical reconnaissance for students in upper secondary school, college and university However, up to now, no study has been found regarding the teaching of technical reconnaissance associated with the profession reality for technical reconnaissance students at Military Science Academy On the other hand, the reality reveals that the teaching of probability and statistics for technical reconnaissance students at Military Science Academy and the profession characteristics of students have started to emerge certain need-to-be-solved questions naming what are going to be taught to students, how are they going to be taught and what kind of knowledge and understanding students need to be provided with to be able to better perform current assigned tasks at their unit These demands directly relate to Probability and Statistics and Information theory; knowledge on Probability and Statistics acts as a foundation and a tool serving the learning of Information theory related subjects and can also have many applications on the practical work When considering students’ occupation requirements, it is necessary for research to be done on teaching Probability and Statistics in the direction of integration with Information theory as for this to be applied to real teaching to train students’ occupational skills Regarding all the reasons above, with the desire to contribute to the improving of Probability and Statistics teaching and learning efficiency at Military Science Academy, we decided on the research topic: “Teaching Probability and Statistics for students on technical reconnaissance at Military Science Academy in the direction of integration with Information Theory” Research purpose Recommending some methods for teaching Probability and Statistics at Military Science Academy in the direction of integration with Information Theory for technical reconnaissance students in order to train their occupational skills Research tasks The study aims at answering the following research questions: - How are the occupation characteristics of experts and students in engineering reconnaissance? - What role Probability and Statistics and Information theory play in engineering reconnaissance? What are the Probability and Statistics and Information theory knowledge needed for the technical reconnaissance major? - What is the basis of choosing to teach Probability and Statistics for students on technical reconnaissance in the direction of integration with Information Theory? - How can Probability and Statistics be integrated with Information theory considering the occupation characteristics of students on Engineering Reconnaissance? What is the integration method here? What is the integrated problem? - What is the reality of Teaching Probability and Statistics at Military Science Academy in the direction of integration with Information Theory? - What pedagogical measures can be proposed about teaching Probability and Statistics in the direction of integration with Information Theory to train occupational skills of technical reconnaissance students at Military Science Academy? - Will the proposed measure be feasible and effective? Will they meet the education and training goals at Military Science Academy ? Research scope The teaching of Probability and Statistics for students on technical reconnaissance at Military Science Academy Research object and focus 5.1 Research object The Probability and Statistics teaching process at Military Science Academy 5.2 Research focus The Probability and Statistics teaching process at Military Science Academy in the direction of integration with Information Theory in order to train their occupational skills Research hypothesis Based on the Probability and Statistics course objective for technical reconnaissance major at Military Science Academy, it can be seen that if being properly constructed and used in the teaching process, the method of teaching Probability and Statistics in the direction of integration with Information Theory can better contribute to the occupational skills training of students on technical reconnaissance at Military Science Academy Research methods The research applies the following methods 7.1 Reasoning method Collecting, synthesizing, analyzing, comparing, carrying out research, systemizing materials on higher education, vocational education and research results as well as documents of the Party, State and Army related to the topic 7.2 Observation method - Collecting, utilizing and processing data for better understanding of technical reconnaissance training at Military Science Academy - Surveying, attending lectures and analysing the current state of teaching Probability and Statistics in the direction of integration with Information Theory before, during and after applying pedagogy measures - Interviewing experts, lecturers and students relating to technical reconnaissance at Military Science Academy about the current situation of learning and teaching Probability and Statistics in the direction of integration with Information Theory and its effectiveness 7.3 Summarizing experiences method - Summarizing colleagues and self experiences in the teaching Probability and Statistics for students on technical reconnaissance at Military Science Academy in the direction of integration with Information Theory 7.4 Professional solutions Consulting experts to clarify some viewpoints about the system of occupational skills of technical reconnaissance soldiers, the quality of teaching Probability and Statistics for students on technical reconnaissance in the direction of integration with Information Theory and the correctness of pedagogy measures proposed in the dissertation 7.5 Case study Choosing a number of students or a group of technical reconnaissance students to observe the progression of occupational skills in Teaching Probability and Statistics in the direction of integration with Information Theory through proposed pedagogy measures 7.6 Pedagogical experiment Pedagogical experiment aims at claiming the feasibility and effectiveness of the proposed pedagogy measures in the dissertation New contribution of the dissertation Teaching Probability and Statistics in the direction of integration with Information Theory serves the occupational training requirements for students on technical reconnaissance at Military Science Academy 8.1 Theoretical meaning - The thesis analyses, clarifies the system of necessary occupational skills for technical reconnaissance students and proposing the system of necessary occupational skills through teaching Probability and Statistics in the direction of integration with Information Theory - The thesis clarified the relation between Probability and Statistics and Information Theory, the role of Probability and Statistics to Information Theory as well as the role of Information Theory to the technical reconnaissance major - Suggest the integration methods and the integration of Probability and Statistics and Information theory - Further clarifying the important role of teaching Probability and Statistics for students on technical reconnaissance in the direction of integration with Information Theory in the current period 8.2 Practical meaning - Building the system of theory and situational exercises about Probability and Statistics associated with Information theory, contributing to the improvement of the ability to practice, the ability to apply, and the training of the occupational skills for students - Proposing forms and process of designing and organizing the teaching of Probability and Statistics in the direction of integration with Information Theory in order to train occupational skills for technical reconnaissance students and designing a number of topics, learning projects illustrating the forms and process above - The thesis proposes some measures in Teaching Probability and Statistics at Military Science Academy in the direction of integration with Information Theory, which have been tested through pedagogical experiment - Enhancing the quality of teaching and learning Probability and Statistics at Military Science Academy to ensure the Academy’s outcome Issues of protection - The perception of teaching Probability and Statistics in the direction of integration with Information Theory to train occupational skills for technical reconnaissance students - The occupational skills needed to be trained for technical reconnaissance students through teaching Probability and Statistics in the direction of integration with Information Theory as proposed are scientifically based and feasible - The proposed pedagogy measures in chapter are feasible in the teaching Probability and Statistics process at Military Science Academy and effective in terms of training occupational skills for technical reconnaissance students 10 Structure of the thesis In addition to the introduction, conclusion, appendices and references, the thesis includes chapters: Chapter The theoretical and practical rationale Chapter Teaching method of Probability and Statistics for students on technical reconnaissance at Military Science Academy in the direction of integration with Information Theory Chapter Pedagogical experiment Chapter THEORETICAL AND PRACTICAL RATIONALE 1.1 Overview of the research problem In Vietnam, there have been many studies on integrated teaching, especially in the field of general education, but so far, very few ones have bên done on integrated teaching in the field of vocational education It can be seen from researching domestic and international studies that most of which has been done on teaching Probability and Statistics for vocational training aimed at developing professional capacity and exploiting the relation between Probability and Statistics knowledge and learners profession knowledge Nevertheless, there has never been any specific research on teaching Probability and Statistics in the direction of integration with Information Theory Especially, exploiting elements of Teaching Probability and Statistics for students on technical reconnaissance at Military Science Academy in the direction of integration with Information Theory has never been mentioned in any study 1.2 Major characteristics of technical reconnaissance students 1.2.1 Training mission and objectives at Military Science Academy - Military Science Academy is responsible for training students in Military Science, engineering reconnaissance, International Relations on National Defense, and foreign languages for the Army One of the priority tasks of the Academy in the current period is training and developing technical reconnaissance - The goal is to train young people and soldiers to meet the standards prescribed by the Ministry of National Defense and become officers with university degrees in military science, engineering reconnaissance, International Relations on National Defense and Foreign languages for the Army Students graduating with technical reconnaissance degrees must well ensure initial functions and missions such as Collecting, researching, processing and publishing news, reporting to superiors 1.2.2 Profession characteristics of technical reconnaissance students Technical reconnaissance studies the ensuring of information communication safety This field uses computers, computer softwares and technical equipment to transmit, collect, store, convert, protect, process, encryption, decryption The main tasks of the technical reconnaissance soldier are to collect enemy information, encryption, decryption information, analyze data, publish news, transmit information, receive information and report the results to the superior commanders To be able to well execute that job, technical reconnaissance students need to be fully and systematically equipped with the knowledge related to the training profession Information theory knowledge (such as knowledge of information transceiver technology, cryptography, information processing analysis) is especially important and directly serves the post-training work, mathematics, linguistics, information technology In which, the theory of Probability and Statistics is one of the courses with many applications for the implementation of the above requirements The origin and core of statistics for technical reconnaissance is the analysis and study of the frequency and the study of languages for encryption and decryption Therefore, Probability and Statistics for technical reconnaissance is mainly used to analyze and research language, its subject is language (plaintext and encoding) 1.2.3 Occupational skills of technical reconnaissance soldiers 1.2.3.1 Skills: Skills are the capability to make use of the existing knowledge and understanding in a creative way to well perform one or many works in order to produce the expected outcome 1.2.3.2 Occupational skills of technical reconnaissance soldiers Basing on the profession characteristics and missions of technical reconnaissance soldiers, it can be stated that: Occupational skills of technical reconnaissance soldiers is the capability to make use of the knowledge, understanding and experience of the technical reconnaissance profession to smoothly and effectively perform the tasks of reception,encryption, decryption, transmission, receiving information, organizing and operating activities for technical reconnaissance teams at the unit 1.2.3.3 Requirements regarding occupational skills of technical reconnaissance soldiers Table 1.1: System of core occupational skills of technical reconnaissance soldiers Group of skills No Occupational skills of technical reconnaissance soldiers Independent working skills Personal skills Cooperative skills Problem solving skills Specialized skills Self-learning skills Language and foreign language skills Data analysing and evaluating and decision making skills Teamwork skills Soldiers management skills Skills on organizing, commanding and operating activities of the technical reconnaissance station Problem solving skills Using technical reconnaissance equipment skills 10 Information Technology skills 11 Information searching and collecting skills 12 Researching, processing and reporting information skills 13 Information encode skills 14 Discovering and decrypting encrypted telegrams skills 15 Consulting and proposing new solutions skills 1.3 Some basic issues about Information Theory and the role of Information Theory in engineering reconnaissance 1.3.1 Definitions 1.3.1.1 Information: Information is a system of messages and commands that reduce the uncertainty of the subject receiving information 1.3.1.2 Relation between uncertainty and probability and If we have to choose an X element in a certain set, such kind of choosing (or "choose" to be understood in a broad sense as trial, inquiry, investigation, reconnaissance, intelligence, etc.) is always uncertain  If the set has only one element, there is no other choice and so there is no uncertainty in that selection  The selection starts to have uncertainty when there are from elements in the set If this number rises, the uncertainty will also rise and the probability and of choosing one element in the set reduces 1.3.1.2 Entrophy Entropy information describes the degree of turbulence in a signal taken from a random event In other words, entropy shows how much information is in the signal with the information being random non-turbulent parts of the signal Entropy is a mathematical quantity used to measure the amount of uncertainty (uncertainty, random quantity) information of a given event or random distribution Entropy of a distribution Assessing X with the following probability and distribution X x1 x2 … xn P p1 p2 … pn Entropy of X is denoted by H(X) and calculated by using the formula: H(X) = If the probal values of X are xi ,1 ≤ i ≤ n, we have : H(X) = In the field of cryptography, the application of entropy to ciphertext examination in a number of specific situations such as if a variate X takes the values in the domain [a, z] according to a probability and distribution P(x), what will be the probability and distribution of the amount of information in the source X? To figure this out, we need to examine entropy H(X) What is the …… of the source X after being encoded into source Y which takes values in the domain [a, z] The examination of H(X) H(Y) is the foundation for evaluating related factors of the cipher system like the code, the security, which serve the process of code discovery Shannon's Entropy Theory states that the linguistic sequence is not a random one but rather a regular occurrence For example, in Vietnamese, after the letter Q must be the letter U, or after the letter A, it cannot be the letter K, but certain words appear with a probability and not necessarily random Just like in English, the Q is always followed by the U Example of Entropy: Supposing that after many years of observing the weather at a specific time, the result are: The weather on the 15th of June (Test A) Possible results of the test Probability and rain 0,4 not rain 0,6 The weather on the 15th of November (Test B) Possible results of the test Probability and rain 0,65 snow 0,15 not rain 0,2 Entropy of these two tests respectively are: H(A) = - 0,4 log20,4 - 0,6 log20,6 = 0,97 H(B) = - 0,66 log20,65 - 0,15 log20,15 - 0,2 log20,2 = 1,28 Since H(B) > H(A), it can be seen that it is harder to forecast that area’s weather on the 15th of November than on the 15th of June 1.3.1.3 Plaintext, encrypted text, key  Plaintext: is the one that need to be encoded  Encrypted text: is the one after being encoded  Key: is the tool to convert from the plaintext to the encoded one and in reverse 1.3.1.4 Cryptography According to Shannon, a cryptography is a set of (P,C,K,E,D) satisfies the following condition: P is a finite set of possible plaintext C is a finite set of possible encrypted text K is a finite set of possible keys For each there is a code rule Each and and a corresponding decryption rule are the one with with every 1.3.2 Information communication model Based on the post-training profession characteristics of technical reconnaissance students and training objectives at Military Science Academy, the model of information communication in technical reconnaissance (including encryption, signal transmission, Information sink and information receive block, cryptanalysis, information outcome) is presented and simulated according to the following diagram (compared with the information communication model from Shannon's point of view, this model clearly shows the training process and main work of students) Transmitter Modulation : encryption Information Source cryptanalysis Communication Channel Blocking receivers Noise Signal transmission Truyền tin cryptanalysis Diagram 1.2 Information communication model in technical reconnaissance Information sink decryption Demodulation Receiver News reports 11 1.4.3 The role of Probability and Statistics in Information Theory and in training occupational skills for Technical reconnaissance students Probability and Statistics is a course that plays an important role in the training program Military Science Academy, Probability and Statistics is the tool and foundation for specialized subjects to train occupational skills for Technical reconnaissance students Considering subjects relating to Information Theory, Probability and Statistics is a mathematical tool mainly used for researching signal transmission and cryptanalysis systems, etc Through researching Information Theory model, the training objective of Military Science Academy and profession characteristics of students, we can identify the following specific roles of Probability and Statistics: Using Probability and Statistics to calculate the frequency of letters in each language Applying Probability and Statistics in encoding the data (the optimal statistical source code of Shannon, Fano and Huffman) and investigating the distribution of characters in a copy Calculates the string match index, using the probability and statistics to calculate the uncertainty of the information Examining and evaluating the quality of an encryption system Applying probability and statistics to cryptanalysis and decryption 1.5 Integrated teaching in profession training for Technical reconnaissance students 1.5.1 Integration Regarding the research scope, through the study of relation between Probability and Statistics and Information theory, we are only going to research and take into consideration the definition of integration in the combination of knowledge and skills between Probability and Statistics and Information theory in order to train occupational skills for Technical reconnaissance students 1.5.2 Integrated teaching 1.5.2.1 General perception on integrated teaching From the concepts of integrated teaching, we can understand: integrated teaching is the orientation of the teaching content and method, in which the lecturers organize and guide learners to mobilize and synthesize knowledge, skills in many different fields to solve learning tasks, thereby forming new knowledge and skills, developing necessary competencies, especially the ability to solve problems in learning and in practice to meet the outcome standards 1.5.2.2 ways to approach integrated teaching Multi-subject integration, interdisciplinary integration, cross-subject integration In this dissertation, the teaching process is approached in the direction of interdisciplinary integration between probability and statistics and Information theory Specifically: - Reviewing the content, probability and statistics and Information theory teaching program to find out the knowledge which is in common and similar, thus, building up interdisciplinary integration teaching topics - Probability and statistics and Information theory are linked to each other and between them, there are topics, examples and exercises applying the common knowledge between Probability and statistics and Information theory - Lecturers organize a learning program surrounding topics, examples, practical problems, learning projects and common problems between Probability and statistics and Information theory, but the concepts or interdisciplinary skills have to be emphasized between subjects, not in individual ones 12 - Combining knowledge between Probability and statistics and Information theory to solve practical problems of the profession through academic projects 1.5.3 The basis for choosing to teach Probability and Statistics for students on Technical Reconnaissance in the direction of integration with Information Theory Basing on the occupation characteristics and occupational skills of technical reconnaissance soldiers Basing on the nature and strengths of integrated teaching Basing on the interdisciplinary knowledge relation between Probability and statistics and Information theory Through researching the content and curriculum of Probability and statistics and Information theory teaching at Military Science Academy, together with occupational skills needed to be trained via teaching Probability and Statistics in the direction of integration with Information Theory, we realize that they have the following knowledge relation, in common knowledge as well as problems with interdisciplinary Probability and statistics and Information theory knowledge: Table 1.10: The interdisciplinary knowledge relation between Probability and statistics and Information theory and the integration problems of teaching Probability and statistics in the direction of integration with Information theory Probability and Information theory Integration problems Training occupational statistics knowledge skills knowledge Information entropy, - Integration through topics - Independent working Variate, Probability string duplication index, such as cryptanalysis skills and of viarate, data compression, alternative coding systems - Cooperative skills Probability and probability and of bits Determine the signal (teamwork skills) calculation rule appearing in codewords, transmission code - Problems solving encrypting data, etc - Integration through projects skills such as cryptanalysis Uni code - Language, foreign The probability and The law of how specific language skills distribution of documents are written - Information Probability and cryptographic key, encryption skills calculation formula Probability and of correct - Integration through -Skills on discovering, ( Bernoulli, Totality, message acquisition when examples, practical math problems, such as Data decrypting the Bayes) interference happens compression by optimal encrypted telegram complete Secure statistical encrypting method - Information searching (Shannon, Fano, Huffman); and collecting skills Probability and The optimal problem in find the probability and - Evaluating and distribution laws of the installation of the distribution of the decision making skills variate, receiving and broadcasting cryptographic key; calculate - Skills on using expectations, systems the probability and of getting softwares relating to the variances, the correct message when there major Statistics, frequency Frequency of the and frequency occurrence of letters in the is noise; examine and evaluate - Skills on organizing, the quality of an encrypting commanding and statistics language, decryption, 13 cryptanalysis Sample theory, parameter estimation, hypothesis testing Evaluate, estimate and verify the information obtained system operating activities of the technical reconnaissance station 1.5.4 Perception and the method of teaching Probability and Statistics for students on Technical Reconnaissance in the direction of integration with Information Theory Regarding the scope of this dissertation, we consider teaching Probability and Statistics for students on Technical Reconnaissance in the direction of integration with Information Theory is a teaching process, in which lectures hold activities for students in order to mobilize the knowledge and skills of Probability and Statistics in combination and integration with Information Theory to solve problems in the profession reality, thus, training the occupational skills for Technical Reconnaissance soldiers For example, lectures hold activities for students to mobilize and synthesize knowledge and skills of Probability and Statistics and Information theory to cryptanalyse the following code: From SOKOMAND to OPETER uni 0300 13/04/1951 0305 13/04/1951 48 3501 3491 79 3492 06 3493 72 3471 7003 3472 49 3472 70 3472 4234 3542 73092 3470 3481 3473 077 3472 49 3472 70 3474 097 3472 49 3470 In this dissertation, considering the supporting role of Probability and Statistics to Information theory and profession reality of Technical reconnaissance soldiers, the knowledge relation and similar knowledge in interdisciplinarity of Probability and Statistics and Information theory, we choose to teach Probability and Statistics integrating with Information Theory in the direction of training occupational skills for Technical reconnaissance students Specifically: - Design some types of statistical probability and lessons integrated with practical professional situations related to information theory to a certain extent in order to train students' occupational skills: New knowledge forming lectures, practice exercises, revision lessons, etc - Demonstrate the integration in some stages or a part of the lesson in the form of + The theory of integration: State and give examples on parts of knowledge of statistical probability and related to information theory + Practical relation: Solve exercises, perform tasks with practical contents, related to knowledge of statistical probability and and information theory - Integrate demonstrated through a number of topics: - Integrated teaching through the increase in organizing for students to practice in units associated with the training major 1.5.5 The process of designing and organizing the theme-based integrated teaching of Probability and Statistics with Information theory Step 1: Select the topic Step 2: Determine the teaching objectives of the topic Step 3: The main content of the topic and make the necessary preparation Step 4: Design learning activities and create a theme-based teaching plan 14 Step 5: Decide on the evaluation tools 1.5.6 Testing and evaluating the learning outcomes of the interdisciplinary integrated teaching process of Probability and statistics with Information Theory - Purpose of testing and evaluation: Helping students identify strengths, improve limitations, realize academic progress, etc - Evaluation point of view: Evaluation of knowledge, skills, and attitudes In which, focus on measuring and evaluating the occupational skills of students - Evaluation content: Demonstrate the integration of probability and statistics knowledge with information theory - Regarding the form of assessment: Written-test, oral test, observations, comments, tests, projects, scientific research, etc - Evaluation criteria are based on: + Learning attitude and ability to take in the knowledge + The ability to apply the knowledge of Probability and statistics to Information theory and in practice after training + The learning results of Probability and statistics and the subject of Information Theory are much related to Probability and statistics of students + The level of occupational skills development of students + Results of the scientific research outcome - Evaluation tools: + Observation evaluation form: Evaluate each cadet or the whole group The evaluation card should be designed in detail, specifically for each stage, each step of the topic or the integrated teaching + Opinion survey form for lecturers, students + Written or oral test (measured on a 10-point scale) 1.5.7 Proposing occupational skills that need to be trained for Technical reconnaissance students through Teaching Probability and Statistics in the direction of integration with Information Theory Foundation for the propose: a) Foundation 1: From the requirements of the outcome standard of technical reconnaissance at Military Science Academy, we have identified the core occupational skills of the Technical reconnaissance soldier (section 1.2.5), including the skills directly related to Probability and Statistics supporting the occupation training for Technical reconnaissance soldier, specifically in two main activities: Activity 1: Code cryptanalysis and decryption Activity 2: Information transmission b) Foundation 2: Based on the necessary factors to promote the effectiveness of the process of teaching Probability and Statistics integrated with Information theory (section 1.5.7), so that it fits the goals and contents of Probability and Statistics subject, lecturers and students at Military Science Academy c) Foundation 3: Experts and specialized subjects lecturers' opinions on Technical reconnaissance sector which assess the opportunity to train occupational skills (Appendix 2) through Teaching Probability and Statistics for students on Technical Reconnaissance in the direction of integration with Information Theory From the above-mentioned bases, we propose the following system of occupational skills that are necessary and can train Technical reconnaissance students through teaching Probability and Statistics in the direction of integration with Information Theory: 15 Table 1.11 Occupational skills that need to be trained for Technical reconnaissance students through Teaching Probability and Statistics in the direction of integration with Information Theory SIGNS SKILLS Skill (KN1) Independent working skills Skill (KN2) Cooperative skills (teamwork skills) Skill (KN3) Problems solving skills Skill (KN4) Language, foreign language skills Skill (KN5) Information encryption skills Skill (KN6) Skills on discovering, decrypting the encrypted telegram Skill (KN7) Information searching and collecting skills Skill (KN8) Data analysing and evaluating and decision making skills Information technology skills (especially the ability to program and use the Skill (KN9) application software related to the major) 1.6 The current situation of Teaching Probability and Statistics at Military Science Academy in the direction of integration with Information Theory 1.6.1 Purpose, content, focus, and method of survey 1.6.1.1 Survey purpose 1.6.1.2 Survey content 1.6.1.3 Survey focus 1.6.1.4 Survey method 1.6.2 Survey results and analysis 1.6.2.1 The current situation of Teaching Probability and Statistics in the direction of integration with Information Theory of lecturers 1.6.2.2 The current situation of acquiring knowledge of Probability and Statistics and students' awareness of the role of Probability and Statistics in Information Theory subjects and work-practice 1.6.2.3 Evaluation of lecturers on the level and effectiveness of using Probability and Statistics in learning Information Theory subjects 1.6.2.4 The current situation of training occupational skills for students through teaching Probability and Statistics General comment: Currently, the curriculum and teaching content of Probability and Statistics have not met the above-mentioned needs of students Information theory has not been integrated at the necessary level in the process of teaching Probability and Statistics for students to see the core meaning of the subject and create favorable conditions for students to learn Information theory subjects From the current perception of lecturers and students about the teaching and learning of Probability and Statistics in the direction of integration with Information Theory and the evaluation of the lecturers who teach the specialized subjects on the applying of Probability and Statistics knowledge of students, we identified a number of concerning problems such as math lecturers need to be equipped with knowledge of integrated teaching and knowledge of Information theory, teaching materials of Probability and Statistics need to be updated to suit the training objectives of the Academy, more content sections related to Information theory need to be added so that students can see the practical meaning of the subject and train the occupational skills Internships are related to practice in biotechnology and the testing and assessing process need to increase the number of questions and exercises related to the practice of the major 16 CHAPTER CONCLUSION In chapter 1, the author has researched the theoretical and practical basis of Teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy in the direction of integration with Information Theory In addition to the analysis and synthesis of the dissertation-related results, the author contributes the following new results: - Proposing the Information Theory model based on the tasks, training objectives, and the occupation characteristics of Technical Reconnaissance at Military Science Academy - Analyzing clearly the role of Probability and Statistics in Information Theory, the relation between Probability and Statistics and Information theory - Proposing the contents (issues) that are integrated into teaching Probability and Statistics to contribute to the training of occupational skills for students on Technical Reconnaissance - Giving opinions on integrated teaching in the training of occupation for students on Technical Reconnaissance, clearly analyzing the advantages of teaching integrated Probability and Statistics with Information Theory for students on Technical Reconnaissance at Military Science Academy - Proposing a teaching method that integrates Probability and Statistics with Information Theory for students on Technical Reconnaissance - Teaching model of interdisciplinary integration between Probability and Statistics with Information Theory for students on Technical Reconnaissance - Proposing the concept of occupation capacity, occupational skills of Technical Reconnaissance soldiers Based on the occupation characteristics, the author proposed core occupational skills of a Technical Reconnaissance soldier with technical skills that need to be trained through Teaching Probability and Statistics in the direction of integration with Information Theory The author has also surveyed and analyzed the current status of teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy, in order to find out the limitations, shortcomings and existing problems in the process of teaching Probability and Statistics in the past as well as present which need to be addressed and adjusted to suit with reality The above research results are the theoretical and practical basis for us to propose a number of Probability and Statistics teaching methods in the direction of integration with Information Theory for students on Technical Reconnaissance at Military Science Academy in chapter Chapter MEASURE FOR TEACHING PROBABILITY AND STATISTICS FOR STUDENTS ON TECHNICAL RECONNAISSANCE AT MILITARY SCIENCE ACADEMY IN THE DIRECTION OF INTEGRATION WITH INFORMATION THEORY 2.1 Measures constructing orientation The measures should adhere to the objectives, contents of the Probability and Statistics training program and must be suitable for students on Technical Reconnaissance The measures must be in line with the current trend of tertiary education teaching method innovation, in order to contribute to the improvement of the training program content.Innovating the teaching method in the direction of integrating Probability and Statistics knowledge with major specialized knowledge, creating opportunities for learners to practice occupational skills 17 Measures need to help students increase their ability to adapt to reality and solve problems arising in practical work in the unit The measures need to promote the activeness in learning of students and must be feasible regarding the condition of Military Science Academy 2.2 Some measures in teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy in the direction of integration with Information Theory 2.2.1 Measure 1: Provide students with basic knowledge of Probability and Statistics in the direction of integration with Information Theory 2.2.1.1 Scientific basis of the measure Basing on the role of Probability and Statistics theory in Information theory and the working practice of students Basing on the survey results on the current learning and teaching for students on Technical Reconnaissance in the direction of integration with Information Theory (section 1.6) Basing on the information communication model in Technical reconnaissance (section 1.3.2): Probability and Statistics is the helpful tool for Technical reconnaissance soldiers in encrypting information and discovering codes Basing on the interdisciplinary knowledge relation between Probability and statistics and Information theory (section 1.5.3.2) Basing on the measures constructing orientation (section 2.1) 2.2.1.2 The purpose and meaning of the measure The measure helps to train the occupational skills including: KN4, KN5, KN6, KN7, KN8, KN9 2.2.1.3 How to implement the measure: a) Technique 1: Provide students with basic knowledge of Probability and Statistics in the direction of integration with Information Theory through the system of theory and situational exercises to meet the Probability and Statistics course objective at Military Science Academy Teaching statistical probability and, on the basis of ensuring the content knowledge under the given time, lecturers need to select and find out which parts of probability and statistics are often used in the work practice or by the subjects of Information theory Thus, selecting examples that aim at the nature and application of probability and statistics to Information Theory To that, lecturers need to compare the content, curriculum between probability and statistics and information theory to find related knowledge and find ways to integrate into each probability and statistics lecture simple knowledge of information theory (using information theory to create situations that lead to the need to use the knowledge of statistical probability and; or, after learning the knowledge of statistical probability and, try to relate and apply information theory) However, in each lesson, it is necessary to remove unnecessary explanation, some items students can read by themselves; build examples, case studies of Probability and Statistics demonstrating the direction of integration with Information Theory; select and rearrange a number of knowledge contents to implement theme-based teaching; add some simple knowledge about Information Theory with direct application of Probability and Statistics, etc For example: - When recalling the knowledge on combinatorial algebra, beside mentioning the definition and addition, multiplication, permutation, matching, combinatorial rules and giving examples on combinatorial algebra, lecturers should add examples whose content relate to Information theory such as Example: From bit and 1, how many words can be created from the 7-bit code that satisfy: 18 a having just bit b having at least bit Through the above example, students can strengthen their knowledge of combinatorics, and have a better understanding of the concept of bits, codewords (before giving the example, lecturers explain to the students the concept of bits and code words) - When teaching about the full probability and formula and the Bayes formula, to associate probability and statistics with information theory, we add the following illustrative example: Example: A station transmits only two signals A and B with probabilities of 0.85 and 0.15, respectively Due to the noise in the transmission line, 1/7 of signal A is distorted and obtained as signal B, while 1/8 signal B is distorted and obtained as signal A Through the above example, students can strengthen their knowledge of the full probability and formula and the Bayes formula, at the same time, students have a little understanding of the signal transmission process, the probability and of obtaining information when there is noise Thus students have initially been trained the occupational skills such as KN1, KN7 b) Technique 2: Provide students with necessary knowledge of information theory to meet the interdisciplinary learning objectives with Probability and statistics Because the knowledge of probability and statistics is often taught before or interwoven with the knowledge of Information theory, so in order to meet the teaching goal of probability and statistics in the direction of integration with Information Theory, it is essential that students must be equipped with the necessary knowledge of Information Theory that has the application of probability and statistics so that students can understand and apply probability and statistics knowledge into practice majors For example, concepts of cryptography, a single substitution cipher, calculation of information uncertainty (Entropy), application of entropy to survey the secure of a ciphertext, Shannon source encryption theory, Fano and Huffman to compress transmitted data, decryption process of a ciphertext based on statistical probability and, etc Example: create source code optimization S = {a1, a2, a3, a4, a5, a6} with probability and {0,3; 0.25; 0.2; 0.12; 0.08; 0.05} 2.2.2 Measure 2: Organize Teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy in the direction of integration with Information Theory 2.2.2.1 The scientific basis of the measure - Basing on the practice of teaching subjects and the major training requirements in the school - Basing on the requirements on the innovation of teaching methods at Military Science Academy which shifts orientation from content-oriented to training occupational skills - Basing on the relationship between Probability and Statistics and Information theory (section 1.5.3.2), the role of the Probability and Statistics theory in Information theory and the occupation characteristics of the Technical reconnaissance soldiers - Basing on the information communication model in Technical reconnaissance (section 1.3.2): Probability and Statistics is an effective support tool for soldiers of Technical reconnaissance in encrypting transmitted information and discovering codes - Basing on the orientation to develop measures (section 2.1) - Based on the survey results on the teaching and learning status of Technical reconnaissance students in the direction of integration with Information theory (section 1.6) 19 2.2.2.2 The purpose and meaning of the measure The measure helps to train the occupational skills including: KN1, KN2, KN3, KN4, KN5, KN6, KN7, KN9 2.2.2.3 How to implement the measure: a/ Technique1: Applying the interdisciplinary knowledge relation between Probability and statistics and parts of the Information theory through examples Regarding this technique, in the teaching process, Information theory is used as an example in Probability and Statistics and Probability and Statistics is used to look for the application in Information theory The purpose of constructing examples and exercises integrating Probability and Statistics with Information theory is to help students get acquainted with future occupations and see that Probability and Statistics plays a role as the basis for providing background knowledge for the major specialized subjects, ensuring the interdisciplinarity of subjects For example, the calculation of the frequency of letters in the language, the number of duplicates of phrases, etc has many applications in cryptographic discovery; distribution of binomial, Bernoulli's formula widely applied in the field of signal transmission; the application of Bayes formula finds the distribution of the code key; the classical probabilistic and expected formula of the variate used in surveying the information uncertainty or the security of an encrypted message b) Technique 2: Assign projects to students to practice, thus, showing the interdisciplinary integration in the teaching process c) Technique 3: Develop interdisciplinary topics integrate probability and statistics with Information theory For example: Topic "CRYPTANALYSIS THE MONOALPHABETIC SUBSTITUTION CIPHER" d) Technique 4: Building and organizing teaching interdisciplinary integration of probability and statistics with Information theory according to themes with support of information technology In this technique, we design the integration topic that links knowledge of probability and statistics with Information theory with the support of Mathlab software for problem-solving in the practical work of Technical reconnaissance soldiers For instance, solving the problem of "determine the code length of the transmission code" 2.2 (Integrate through practice): Organize practicing activities for students and practice in military Measure units associated with training major through the study of probability and statistics 2.2.3.1 Scientific basis of the measure According to teaching theory in Military schools, the method of military tertiary education is associated with the training profession of military universities and academies; Attached to military construction and combat practices, etc 2.2.3.2 The purpose and meaning of the measure The measure helps to train the occupational skills including: KN1, KN2, KN3, KN4, KN6, KN7 2.2.3.3 How to implement the measure: a) Technique 1: Require students to some study about the Technical reconnaissance profession and the applications of Probability and Statistics in the major through organizing students' meetings with specialized lecturers and instructing students to read some documents related to Probability and Statistics b) Technique 2: Let students practice in military units associated with their major through the learning of Probability and Statistics 20 Example: In this dissertation, I choose to teach the lesson "Frequencies of random variables", specifically: Organize teaching in projects with the topic "Law of the writing of some specific documents" 2.2.4 Measure 4: Adjust the content and method of testing, evaluating learning results in the direction of training occupational skills for students on Technical Reconnaissance 2.2.4.1 The scientific basis of the measure 2.2.4.2 Purpose and meaning of the measure This measure aims at measuring changes in the occupational skills of students 2.2.4.3 How to implement the measure a) Regarding the evaluation content (structure of questions and exercises): We orient to build a system of questions and exercises to test and evaluate learning results in many aspects, requiring students to meet the following request:  Students are required to master the learned knowledge and have skills to solve typical exercises in the Probability and Statistics subject  Students are required to understand and know how to solve Probability and Statistics problems related to Information theory subjects and post-training practice  Initially apply in real-life problems and practical work at a simple level  The content of the essay, study project or study topic has an association between Probability and Statistics knowledge and Information theory and practical work to train vocational skills for students b) Regarding the form of examination and evaluation: - Regular testing and evaluation Periodical testing and evaluation Examination and evaluation at the end of the semester (the final exam) Discussion, essay, etc, 2.2.5 Measure 5: Renovate professional activities to foster math lecturers the necessary knowledge and skills to teach Probability and Statistics in the direction of integration with Information Theory 2.2.5.1 The scientific basis of the measure 2.2.5.2 Purpose and meaning of the measure The measure helps Probability and Statistics lecturers improve their professional qualifications, promote the effectiveness of integrated teaching, and perfect their pedagogical skills Lecturers, thus, know how to fully exploit the knowledge of Probability and Statistics applied in the training major and especially in Information theory subjects, and bring that interdisciplinary knowledge to equip students at Military Science Academy in a more complete and accurate way 2.2.5.3 How to implement the measure a) Seminar in mathematics: b) Organize an interdisciplinary seminar between mathematics and Information theory subject c) Math lecturers self-research material on Information theory teaching in the training major of students and consult experts in the field of Information theory CHAPTER CONCLUSION On the basis of theoretical and practical research results presented in Chapter and Chapter 2, the dissertation has oriented and proposed to build measures of teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy in the direction of integration with Information Theory, including: Measure 1: Provide students with basic knowledge of Probability and Statistics in the direction of integration with Information Theory 21 Measure 2: Organize Teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy in the direction of integration with Information Theory Measure (Integrate through practice): Organize practicing activities for students and practice in military units associated with training major through the study of probability and statistics Measure 4: Adjust the content and method of testing, evaluating learning results in the direction of training occupational skills for students on Technical Reconnaissance Measure 5: Renovate professional activities to foster math lecturers the necessary knowledge and skills to teach Probability and Statistics in the direction of integration with Information Theory The structure in each measure includes the Scientific basis of the measure, its purpose, meaning along with how to implement the measure and examples The examples given in the dissertation are related to Information theory and post-training practice of Technical reconnaissance students, thereby helping them see the nature of the job and at the same time form the necessary capacity that will, later on, be needed The abovementioned measures contribute to training the occupational skills for students as well as the ability to apply probability and statistics in new situations that learners encounter in life From the above mentioned pedagogical measures, lecturers can apply them in Teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy In addition, lecturers can continue to exploit similar examples to suit the training subjects in order to improve teaching efficiency and create conditions for students to be trained on occupational skills This confirms the feasibility of the proposed measures and is in line with the training objectives at Military Science Academy Chapter PEDAGOGICAL EXPERIMENT 3.1 Purposes, requirements, missions, and principles of the organizing of the experiment 3.1.1 Experimental purpose - Test the scientific hypothesis of the thesis - Evaluate the feasibility and effectiveness of the measures proposed in the dissertation according to the following criteria: 3.1.2 Experimental requirement 3.1.3 Experimental mission 3.1.4 The principles of the experiment 3.2 Time, place, and pedagogical experimental subject Due to the characteristics of Military Science Academy, in which each course only enrolls one full-time class of Technical reconnaissance major and there are not enough students to be divided into two experimental classes, so we choose to teach pedagogical experiment using the case-study method Pedagogical experiment round 1: Conducted in the academic year 2017 - 2018, class 35TS with 25 students on Technical Reconnaissance at Military Science Academy The experimental process was continued in the school year 2018-2019 through monitoring some typical cases Pedagogical experiment round 2: Conducted in the academic year 2018 - 2019, class 36TS with 32 students on Technical Reconnaissance at Military Science Academy 3.3 The method of pedagogical experimental 3.3.1 Investigation method 3.3.2 Observation method 22 3.3.3 Mathematical statistical methods 3.3.4 Case study method 3.3.5 Building evaluation methods and criteria 3.3.5.1 Qualitative evaluation method and criteria Processing questionnaires collected from lecturers and results from practice observation through pedagogical experiment activities to evaluate the ability to absorb new knowledge, the ability to apply probability and statistics knowledge in specialized subjects and in real-life situations; the level of occupational skills development of Technical Reconnaissance students through teaching Probability and Statistics in the direction of integration with Information Theory 3.3.5.2 Quantitative evaluation methods and criteria Criterion 1: Students' probability and statistics learning results  Measuring tools: Curriculum test, the final exam whose content test the integration of probability and statistics knowledge with information theory knowledge The exam structure (see in measure 4)  Scale: According to a scale of 10 Criterion 2: The level of occupational skills development of students through learning projects Measuring tools: The scoreboard following the criteria of the learning project implementation process which shows students’ occupational skills development level In the first round of the pedagogical experiment, students work on the project "Law of the writing of some specific documents" In the second round of the pedagogical experiment, students work on the project "discovering the USA-South Korea coalition Uni-code" Scale: To evaluate the progress and proficiency of the occupational skills, we use a-4-level scale: good, fair, average, weak corresponding to each evaluation criteria that we propose 3.4 Experimental content 3.4.1 Pedagogical experiment materials  Teaching plans, lesson plans for integrating probability and statistics with information theory  The questionnaire survey of lecturers (maths and specialized subjects lecturers) and technical reconnaissance students, students tasks achievement evaluation form 3.4.2 Training maths lecturers at Military Science Academy on Teaching Probability and Statistics in the direction of integration with Information Theory (experiment with measure 5) 3.4.3 How to conduct pedagogical experiments The pedagogical experiment was conducted through two independent rounds as follows: + Round 1: Experimental teaching of measures 1, 2, 3, and through teaching and learning activities of probability and statistics on the experimental model is the 35TS class at Military Science Academy with 25 sophomore students After the first round, we pick out students of class 35TS for an in-depth experiment by assigning the research topic: "Applying probability and statistics in some classical coding systems" + Round 2: Experimental teaching of measures 1, 2, 3, and through teaching and learning activities of probability and statistics on the experimental model is the 36TS class at Military Science Academy with 32 sophomore students The pedagogical experiment round helps to test the content proposed in the pedagogical experiment purpose 3.5 Results of the pedagogical experiment 3.5.1 Analyze the qualitative results The proposed measures are reasonable, sticking to the target, content, training program of probability and statistics at Military Science Academy, suitable for Technical Reconnaissance students The proposed 23 pedagogical experiment has high feasibility, in accordance with probability and statistics course objectives and the training objective for Technical Reconnaissance students at Military Science Academy The teaching process according to the proposed measures has helped to fully equip the knowledge, skills, and techniques of probability and statistics and better train the students' occupational skills 3.5.2 Analyze quantitative results Through the collected data, it can be seen that the occupational skills of the students have developed according to levels Before the pedagogical experiment, the assessment criteria of students were mainly on weak and average levels due to the fact that students were not familiar with the occupation practice However, through teaching probability and statistics in the direction of integration with information theory, especially through learning projects, students are trained in occupational skills and have access to practical situations, thus, enhancing the occupational skills This creates favorable conditions for students to study well the next specialized subjects and improve their ability to apply learned knowledge to practical work in the unit 3.5.3 Evaluate the cognitive progress, the ability to apply probability and statistics knowledge in the major and the proficiency level of the occupational skills of students through a number of typical cases Through the monitoring of the post-pedagogical experiment, all students in the case study made clear progress, the occupational skills of these students developed to higher levels Especially the specialized skills, as in the beginning, the students did not know anything about the encrypting, decrypting, cryptanalysis skills of coding, but the process of pedagogical experiment has helped to train those skills better, students understand about the occupation and were able to perform some practical work in the unit CHAPTER CONCLUSION Pedagogical experimental results allow us to draw some conclusions as follows: - The pedagogical experimental proposed in the dissertation, which can be implemented in the process of teaching Teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy and has shown some initial effectiveness, contributed to help students master the knowledge, skills and techniques of Probability and Statistics The students' ability to apply Probability and Statistics knowledge in their major has been improved, and so has the quality of learning Probability and Statistics - The synchronous application of the measures and the techniques of implementing the measures have helped students well perceive the knowledge of Probability and Statistics and Information theory, thereby creating conditions for students to be trained in necessary occupational skills The experimental results show the positive trend of development in the levels of occupational skills, which confirms the correctness of the proposed research purpose and proves the scientific hypothesis of the dissertation The research mission is completed, the proposed measures are completely feasible and can be applied in teaching Probability and Statistics for students on Technical Reconnaissance at Military Science Academy in the following years CONCLUSION AND RECOMMENDATION I CONCLUSION Through theoretical and practical research, the dissertation has obtained the following main results: 1) Provide the definition of occupation capacity, analyze and clarify the occupation characteristics of the Technical reconnaissance soldiers Researched and synthesized the system of 15 necessary occupational skills of Technical reconnaissance soldiers and proposed occupational skills of Technical reconnaissance soldiers that can be trained, formed and developed through teaching Probability and Statistics in the direction of integration with Information Theory 24 2) The dissertation has summarized some of the basic Information Theory matters and the role of Information Theory in training objectives of Military Science Academy and based on the characteristics of the occupation, the thesis has proposed the model of Information Theory associated with the occupation in training Technical reconnaissance students 3) Present an overview of matters of integration and integrated teaching in the training of occupation for students on Technical Reconnaissance at Military Science Academy Research and clarify the bases for choosing to teach Probability and Statistics in the direction of integration with Information Theory 4) Research the contents, programs, textbooks of Probability and Statistics associated with the occupation of Technical reconnaissance students The dissertation has analyzed and clarified the relationship between Probability and Statistics and Information theory, the role of Probability and Statistics in Information theory and proposed integration of Probability and Statistics and Information theory to train occupational skills for Technical reconnaissance students 5) Through studying the current situation of teaching Probability and Statistics in the direction of integration with Information Theory at Military Science Academy, the dissertation has analyzed and clarified some of the teaching's basic features and revealed current shortcomings, limitations that need to be innovated in teaching Probability and Statistics This is one of the scientific bases to propose measures of teaching Probability and Statistics in the direction of integration with Information Theory at Military Science Academy to train occupational skills for Technical reconnaissance students 6) The dissertation proposes measures and teaching techniques of teaching Probability and Statistics in the direction of integration with Information Theory and organized pedagogical experiment to illustrate the feasibility and effectiveness of proposed pedagogical measures The pedagogical experimental results show that the proposed pedagogical measures are feasible and produce good results II RECOMMENDATION To enhance the association between the content, the curriculum Mathematics courses (especially probability and statistics) and other subjects in the training program system at Military Science Academy (especially the subjects about Information Theory), I propose some following recommendations : - It is necessary to foster math lecturers with knowledge of Information Theory to ensure the integrated teaching of Probability and Statistics and Information theory - Lectures need to renovate the aims (knowledge, practice of occupational skills) in the teaching process of Mathematics courses in general and the Probability and Statistics in particular - Military Science Academy should recompile textbooks, teaching materials for Mathematics subjects in general and the Probability and Statistics course in particular in the direction of integration school with Information theory to train occupational skills for Technical reconnaissance students 25 PUBLISHED SCIENTIFIC WORKS RELATED TO THE DISSERTATION Nguyen Van Dai (2016), Teaching probability and and statistics in the direction of integration with the majors trained at Military Science Academy, Journal of Education and Society, No 6, April, p 98-101, 109 Nguyen Van Dai (2017), Teaching probability and and statistics for students in Technical Reconnaissance at Military Science Academy, Journal of Education, No 420, December, pages 27-30 Nguyen Van Dai (2018), Teaching probability and and statistics in the direction of integration with information theory for students majoring in Engineering at Military Science Academy, Journal of Educational Science, No 08, August, pp 101-106 Nguyen Van Dai (2019), Applying interdisciplinary integrated teaching in teaching Probability and and Statistics at Military Science Academy, Journal of Educational Science, January 13, pp 104-109 Nguyen Van Dai (2019), Theoretical basis for determining the content and teaching methods of Probability and and Statistics subject for Technical Reconnaissance major at Military Science Academy, National Intelligence Science Journal room, number 30, March, pp 80-86 ... into Information theory) Cutting out some unnecessary demonstration; selecting and organizing parts of the knowledge to operate theme-based teaching Adding some simple Information theory knowledge... searching and collecting skills 12 Researching, processing and reporting information skills 13 Information encode skills 14 Discovering and decrypting encrypted telegrams skills 15 Consulting and proposing... a regular occurrence For example, in Vietnamese, after the letter Q must be the letter U, or after the letter A, it cannot be the letter K, but certain words appear with a probability and not