Accesso libero

Relevance recommendation method based on multimedia technology-assisted English teaching design and teaching content

  
27 feb 2025
INFORMAZIONI SU QUESTO ARTICOLO

Cita
Scarica la copertina

Introduction

Education has always been the goal that our country must achieve. The significance of education to the country is far higher than the benefits brought by other undertakings. The benefits brought by education are long-term. It points out the direction for generations of people and guides them to establish the correct three view. But at present, the development of education in China is relatively slow. Under the requirements of society, education must find a way to lead it further. At this time, multimedia technology was introduced. The research on multimedia technology is earlier than in China. At the beginning of the 20th century, some foreign countries took the lead in applying the technical methods of multimedia electronic technology to education. The perfect results of earlier countries have induced other countries to imitate the educational undertakings, and this situation has led to the rapid development of modern educational technology. In the 21st century, in addition to the well - known rapid development of science and technology, multimedia technology has also developed rapidly at home and abroad. The emergence of multimedia has changed the original teaching method, and it has injected new blood into the teaching cause. In terms of English teaching design, multimedia provides clear and complete audio that allows students to understand the pronunciation, and images and videos can also stimulate students' interest. In terms of teaching content, the emergence of multimedia can make teaching content in line with social, national and international situations. Multimedia courseware can also help teachers sort out the knowledge system more clearly, improve students' attention in class, and improve teaching efficiency. The emergence of multimedia technology can assist the further development of teaching update.

Auxiliary method of multimedia technology in teaching

American educator Dell put forward the famous audio-visual teaching theory [1], which is also known as the "Tower of Experience" theory. The Tower of Experience is shown in Figure 1:

Figure 1.

Tower of Experience

In the audio-visual teaching theory, it is divided into ten levels and three experiences according to the degree of abstraction of teaching experience. Among them are language symbols and visual symbols in the upper-level abstract experience, indicating that students' perception needs to be expanded in teaching. In the experience of observation, movies and television, radio recordings, images and photos, etc., indicate that it is necessary to combine modern multimedia technology in teaching to display boring book knowledge through multimedia. The application of multimedia can promote the innovation of teaching and promote the development of education.

Multimedia -assisted English teaching design

In the widespread use of multimedia in teaching, English has taken a big step forward by introducing multimedia to students, for example, playing video, playing audio, making courseware, etc. to increase students' interest in new subjects. In the English class, teachers play more recordings for students to follow and read to achieve the purpose of accurate pronunciation. The audio processing process is shown in Figure 2:

Figure 2.

Audio processing flow chart

When processing human voice, in order to remove the influence of vocal cords and lip vibration, increase the main content of the voice, and make the voice clearer, the voice is pre-emphasized, and the high-pass filter [2-3] processing process is shown in formula 1 shown: xp(n)=x(n)k(n1)

Where the K value is any number between 0 and 1, but is usually chosen in studies between 0.9 and 0.97 to achieve the best processing results. Because the computer processing signal limits the length of the experiment, the campus is windowed during the operation, and the window is processed to achieve continuous audio. The goal is to perform Fourier expansion [4-5] to avoid the Gibbs phenomenon. The operation method of adding a window is shown in formulas 2 and 3: S(n)=S(n)×W(n) W(n,a)=(1a)a×cos[ 2πnN1 ],0nN1

When the Hamming window parameter a = 0.46, W (n) is calculated as shown in Equation 4: W(n,a)={ 0.540.46×cos[ 2πnN1 ]0nN0others

The zero-crossing ratio is a simple way of working with audio, and it represents the rate at which the signal changes. It is widely used in speech recognition and music recognition by listening to music. Teachers will apply this method to students' assignments such as reading dubbing. It is shown in formula 5: zcr=1T1t=1T1{ stst1<0 }

Where s is a signal of length T. In this method, the zero-crossing rate is an effective pitch detection method.

Multimedia technology network information sharing

There are several user terminal devices with communication capabilities in the campus, such as teachers' computers or multimedia in classrooms. These devices together constitute a D2D cache network [5-6], which caches information to achieve the purpose of user information sharing. Let U be all users in λ the school, and be the user density in the school. In a circular plane with a radius of R, the distribution of the number of D UEs included is calculated as shown in Equation 6: PR,λ(X=n)=(λπR2)πeλπR2n!

When performing information sharing, the effective transmission distance is R, and only when the distance between users is less than R can a D2D communication link be established between D UEs to achieve information content sharing. The technology of information content sharing helps teachers to obtain learning materials and understand the progress of each class.

D UE is in the cache benefit stage in the D2D cache. At this stage, the D UE will try to find the required information in the device and surrounding devices. There are three results in the information search stage: self-hit, D2D cooperative hit and miss. Because the search is inaccurate, the cached information needs to be sorted and collected to improve the hit rate. Let the cache collection be F, and find f in the collection F, then the probability of f being accessed is as shown in formula 7: Pf=iγj=1|F|jγ

Among them, the parameter γ is the distribution of body popularity distribution in multimedia content Zipf [7-8]. Because caching many files with the same content in a single D i=1|F|nUM UE will not improve the cache hit rate, constraints appear to act on the D UE. The proportion of users who cache the content f to the total users is the probability of hitting the content f in the D iUE. The probability calculation is shown in Equation 8: P(ri,fself|rf)=nfU

Under the D2D cooperative hit condition, for a single D UE, within the effective transmission range of D2D, the number of other D UEs satisfies the Poisson distribution. That is, when the D UE issues a query request for the file f, at least one user within the effective range of the D 2D has cached f.

The cache D UE distribution of file f obeys nfUλ the two-dimensional parameter of HPPP, so the calculation method of the number of users who have replaced file f within the effective transmission range of D 2D is as shown in Equation 9: PD2D(hit=n)=(nfUλπR2)nenfUλπR2n!

Cooperative fate occurs under the condition of self-hit, that is, the D UE probability that at least one user has the desired content in the feasible area of the D UE is calculated as shown in formula 10: PD2D(hit1)=1enfUλπR2

The calculation of the probability of the occurrence of cooperative hit content f is shown in Equation 11: PD2Dhit,f=(1Pselfhit,f)(1PD2D(hit1))=(1nfU)(1enfUλπR2)

When a user requests a query for the content f, the calculation of the probability that the D UE can obtain the file f from the multimedia information cache network is shown in Equation 12: Phit,f=(1nfU)(1enfUλπR2)+nfU

As can be seen from the above, according to the distribution of the popularity of multimedia content Zipf, the probability that the shared content f in the campus is requested to be queried can be expressed. From this, it can be obtained that the general cache hit rate in shared multimedia can be expressed by Equation 1.3 as follows: Phit=c=1|F|Pr,fPhit,f

As can be seen from the above, the choice of the optimal caching method depends on the popularity of the known content.

The auxiliary role of multimedia technology in teaching

For example, Chinese, English, politics, history and other subjects must not be taught blindly in the process of teaching, which will weaken the interest of students and lead to the failure of the efficiency of listening to the teaching purpose. In the process of learning these subjects, multimedia when used properly, the most common method is to make courseware ppt. Bright images and interesting videos in the courseware can improve students' attention and are more conducive to students' learning. The interactive courseware production process is shown in Figure 3:

Figure 3.

Interactive courseware production flow chart

In the process of making courseware, images are more important, and knowledge-related images in a good courseware are essential, but the large memory of images is a troublesome part of making courseware, so it is necessary to compress images. Less. Compressed sensing theory is an emerging signal processing paradigm that encodes sparse signals with fewer observations than other methods. CS technology [9-11] can complete the compression of image information, improve the speed of image signal sampling and compression, and can better handle image signals with a large amount of data.

The size of the M × N rectangular array is Φ, the compression of the signal X of length N is shown in formula 14: y=ΦX

Where y is the measured value of the formula. X is the value to be measured. If the X signal itself is not sparse, the size of N × N the orthogonal sparse basis Ψ , Ψ is expressed as Equation 15: X=Ψs

Where s is the sparsity representation of X under. Ψ

In the process of multimedia technology-assisted teaching, image compression can be better reflected in the use of multimedia, and interactive courseware can make students feel the atmosphere and happiness of learning.

Improvement of Multimedia Assisted Teaching Method

When the multimedia is transmitted, the large and small files may cause data loss due to various reasons. In this case, the compiler is required to encode and decode the lost datagrams, so as to restore the important information in the multimedia. Raptor codec is usually selected in the codec to process multimedia data.

Transmission of multimedia data packets

At the encoding end of LT, we divide the file to be transmitted into multiple original data of equal amount. According to the encoding algorithm, encoding symbols can be generated, and the decoding end receives the encoding symbols. If the encoding end stops sending the encoding symbols, the file transmission is successful. The encoding process of LT is shown in Figure 4;

Figure 4.

encoding flow chart of LT

In the decoding process of the LT code [10][12], the response to the symbols in the first half is relatively fast, and the method can start to work after receiving a small number of data packets, but the code will be excessively processed in the last part of the compilation. The situation of untimely data accumulation. If the original data packet with too large data is directly received, the remaining codes that have not been decoded will flood out and cause avalanche decoding. Then the ratio of the received quantity to the original data quantity, the decoding overhead of the fountain code is shown in Equation 16: ε=NKK

Among them, K is the number of original data packets, and N is the encoding packet when the compilation is successful. The performance of the fountain code is usually measured by the decoding overhead. The smaller the overhead, the better the performance of the fountain decoding.

The original LT code is an ideal distribution function of the solitary wave distribution, and its expression is as in Equation 17: { p(d)=1kd=1p(d)=1d(d1)d=2,3k

It can be seen from the formula that this hypothetical ideal wave has an encoding packet with a degree value of 1. Through the calculation, there are continuous encoding packets of 1 appearing and entering the calculation until all the encoding packets are compiled to achieve the transmission of information in multimedia. However, in the actual operation, if no encoding packet of 1 is found, subsequent deciphering cannot be performed, so this method is not commonly used in actual operations.

The ideal solitary distribution function is improved, and a robust solitary distribution function [13-14] is proposed. The calculation method is shown in Equation 18: τ(d)={ T/(dk)d=1,,k/T1TLn(T/δ)/Kd=k/T0d=k/T+1,,k

Where s is a variable constant and δ is the probability of a calculation error, and T is the mean of the encoded arrays representing the degree value of 1. The function R SD is obtained by adding and combining the two distributions, and its calculation is shown in formula 19: RSD=ρ(d)+τ(d)d1k(ρ(d)+τ(d))d=1,2,,k

Although the robust solitary distribution function is more complicated than the previous method, it increases the robustness of decoding and helps the decoding process to be more stable.

When constructing Raptor code, a new function fixed allocation function is proposed, and when K is less than 65536, its function expression is shown in formula 20: Ω=0.007969x+0.493570x2+0.166220x3+0.72646x4+0.082558x5+0.056085x8+0.037229x9+0.055590x19+0.025023x65+0.003135x66

Among them, the average value of the fixed degree distribution is 5.8703. Because of the characteristics of the fixed distribution function, all this function is usually used in the case of long coding LT codes, and the longer the code length in the data packet processing process, the better the effect of this method.

In the robust solitary wave distribution, there will be a truncation phenomenon, and the maximum value D is set. If d in the robust solitary wave distribution function is greater than D, it is called truncation. The truncated data needs to be unified. This is called the truncated robust solitary distribution function and its expression is shown in Equation 20: f(d)=RSDd=1DRSDd=1,2,,D

The truncated robust solitary function removes the larger value in the robust solitary distribution, improves the probability of selecting a smaller degree value, and reduces the average degree value. This operation reduces the complexity of coding and decoding, which improves the ability to compile. The better the compilation performance, the better the compilation effect of the data package. In the auxiliary design of multimedia for teaching, the higher the compilation performance, the more complete the data in the data package, and the teaching-related materials will be guaranteed.

Application of Raptor Code in Multimedia

In Raptor, D is the input symbol; C is the symbol between pre-coding and coding of D; E is the symbol after L and T of C ; T is the output symbol. In the first part of the encoding, n symbols are added before D = [Zn, T]T the data paceet to form a combination T[t0, t1,…, tK–1] of D input symbols and the inverse matrix of A through processing to obtain L, where C = [C0, C1,…, CL–1]T the calculation of the intermediate symbols is shown in formula 2 2: C=A1D

In the second part of the encoding, LT is performed on C, and C and GLT(1,2, ,N) is operated to generate the encoded symbol E = [e0, e1,…,eN–1]T, then the calculation of E is shown in formula 23: E=GLT(1,2,,N)C

where, GLT(1,2, ,N) let the matrix size be N × L .

The index will be added when the symbol is received, and the index of the higher data packet will be added to each data packet, and the corresponding matrix will be constructed according to the index of the coded symbol, GLT(1,2, ,N) which is M = N + S + H formed by combining with other matrices AM×L. The intermediate symbols C = [C0, C1,…, CL–1]T need the help of Gaussian elimination method [15-16] to solve, and its method is shown in Equation 24: D=AM×LC

In the second part of the decoding, the intermediate symbol is decoded, and if the decoding is successful, all the data is restored. The calculation method is shown in formula 25: T=GLT(1,2,,N)C

where is GLT(1,2, ,N) a matrix of size K × L.

Multimedia recommendation for the relevance of teaching content

According to the students' learning methods, enowledge, media preferences and interest preferences, teachers need to use multimedia to formulate learning methods that suit their students' conditions, and match the students' recommendations as shown in Figure 5:

Figure 5.

Student-Specific Referral Flowchart

According to the process in the figure, the interests and preferences of the students can be well understood, and the multimedia can recommend the students according to the information in the system.

The learning speed of students under the recommendation of multimedia teaching content is shown in formula 26: lspeed=Ni=1MSCSii=1nSCSi

where N represents the people who study the content and i=1MSCSi is the sum of the time students study, and lspeed is the average speed of all students learning. According to the above formula, the judgment of students' learning ability can be deduced, as shown in formula 27: LA=grade/agrade

Among them, LA is the ability of students to learn the knowledge, grade is the final grade of students learning this knowledge, and agrade the average grade of all students learning this knowledge point. The evaluation index of L A is 1. If the value is greater than 1, the student's ability is in the middle and upper class, if it is equal to 1, it is medium, and if it is less than 1, it is low.

According to the interests and preferences of each student, the teacher recommends the teaching content based on the multimedia technology and formulates the learning method in line with the students, which can effectively improve the students' learning ability.

Simulation experiment of teaching design and content with the aid of multimedia technology
Transmission of teaching video in multimedia

In the process of video transmission, there will be a probability of loss of encoded packets. This event will lead to incomplete video communication and the use of multimedia is not the most effective. During the simulation, the original data is divided into 100 groups of the same amount, and the video data packets will be converted into videos by the V CL multimedia player [17-18], and then flow into the network to be sampled by the teacher and used in teaching. The model adopts 6000 video data packets for transmission, and the final results obtained by the general statistical analysis of the encoded packets and the packet loss rate are shown in Table 1 and Figure 6:

Number of encoded packets and packet loss rate in video transmission

Packet loss rate (%) 20 30 40 50 60 70 80
Direct connection without coding 67 107 160 214 296 403 472
Number of encoding packages 100 16 15 13 33 51 74 94
Number of encoding packages 105 13 16 13 12 15 18 23
Number of encoding packages 110 15 13 14 14 14 13 14
Number of encoding packages 115 14 14 15 15 13 17 15
Figure 6.

Number of encoded packets and packet loss in video transmission

As can be seen from the above table and figure, the number of lost packets of uncoded direct connection is greater than that of other codes. And no matter whether the packet loss rate is higher for encoding and transmission, the more data packets are lost, which affects the transmission of video to a certain extent.

the L W-EZEP model, compare the performance of the improved model, simulate two C ITY and S OCCER video sequences respectively, and reconstruct the video in multimedia to ensure that the quality of the frames in each layer is improved. , because the 0th frame of the base layer frame does not participate in the bit rate allocation, the quality of the frame in the first G OP [19-20] is not improved much, and the video quality is not improved much, then L W-EZEP and its improved model are in two sequences. The comparison is shown in Table 2, and the performance comparison of the two sequences is shown in Figure 7:

Comparison between the two-sequence L W-EZEP model and its improved model

PSNR-Y PSNR-U PSNR-V average PSNR
CITY sequence LW-EZEP model 33.52 41.75 43.46 34.55
improved model 34.34 42.21 43.89 37.24
SOCCER sequence LW-EZEP model 33.83 41.19 42.45 36.51
improved model 34.21 41.76 43.02 36.95
Figure 7.

Comparison of the original model and the improved model between the two sequences

It can be seen from the above figure and table that the improved models of the two sequences have higher P SNR values than those before the improvement, indicating that the video processing is better and it is used more in multimedia video. Because the change in the first stage is not very large, it is shown in the image that the curves at the front end are relatively close.

According to the above two sequences to study the performance of the video distribution system, take the first 40 frames of the video as the distributed video source, and distribute to 5 teachers. The signal-to-noise ratio of 3 teachers is 2 dB, and the signal-to-noise ratio of 2 teachers is 2dB. The ratio is 1.5dB, which correspond to medium-speed, high-speed, and ultra-high-speed access. The performance comparison of video distribution based on the slope search algorithm [21-22] is shown in Table 3 and Figure:

Slope search algorithm for video distribution performance comparison table

SNR (dB) Target rate (kbps) Actual rate (kpds) PSNR-Y PSNR-U PSNR-V average PSNR
CITY 1.5(1) 1000 995.4 35.3 42.6 44.2 37.9
1.5(1) 1500 1499.4 36.8 43.8 45.3 39.4
2(1) 450 430.2 32.1 41.1 42.8 35.4
2(1) 1000 1008 35.6 42.9 44.5 38.3
2(1) 1500 1452.7 36.9 43.8 45.3 39.5
SOCCER 1.5(2) 1000 981 35.1 42.3 43.6 37.6
1.5(2) 1500 1468.8 36.5 43.5 44.8 39.1
2(2) 450 450 32.6 40.3 41.6 35.4
2(2) 1000 1002.6 35.2 42.5 43.8 37.8
2(2) 1500 1427.4 36.7 43.5 44.8 39.2
Figure 8.

Comparison of video performance of two sequences under the algorithm

It can be seen from the table that under the two sequences, the actual rate is not much different from the target rate under each signal-to-noise ratio, which is more in line with ideal data. The data in the above example proves that under the same signal-to-noise ratio, high-speed access is better than medium-speed access, and ultra-high-speed access is better than high-speed access. When teachers use multimedia, they should adopt a high-speed access method to ensure the completeness of the video.

Evaluation of images in the application of multimedia in teaching

For example, the experience tower theory proposed by American educator Dell, teaching needs to combine visual symbols, so the reasonable processing of images in the process of integrating multimedia into teaching is essential, and images can enhance the interest of the classroom. Converting words into images can more vividly express the atmosphere and artistic conception expressed by the words. The indicators for evaluating images are usually P NSR and S SIM. In the table below, UEP [23-24] uses unequal protection, E EP uses homogeneous protection, and the image quality evaluation indicators for multiple runs of the two the model results are shown in Table 4 and Figure 9 below:

Image quality evaluation comparison table

method UEP-Raptor EEP-Raptor
PSNR(1) SSIM(1) PSNR(2) SSIM(2)
1 32.98 0.91 9.08 0.27
2 32.87 0.89 24.71 0.85
3 33.11 0.90 29.57 0.86
4 32.58 0.90 5.56 0.24
5 31.33 0.89 27.38 0.73
Figure 9.

Image quality evaluation comparison chart

It can be seen from the above table and figure that in the results of multiple simulations of the image, the P SNR value of the image in the U EP evaluation is 3 3.11 at the highest, 3 1.33 at the minimum, 0.91 at the maximum and 0.91 at the minimum SSIM value 89, the difference between the two is not big, indicating that the evaluation of the image by U EP is not much different from the one-time simulation. In the EEP evaluation, the maximum value of P SNR is 29.57, the minimum value is 5.59, the maximum value of SSIM is 0.86, and the minimum value is 0.24. In the E EP evaluation, the maximum and minimum values of both P SNR and S SIM are quite different, which is inconvenient for image processing, so U EP-Raptor is selected between the two.

The use of multimedia in teaching and students' perspectives

With the rapid development of networe technology today, the education of students should not stop at the traditional way of education. The society calls on schools to apply multimedia to the education of students. Multimedia can assist in designing and teaching English, expressing English words to students in a more novel way, and giving English audio to students so that students can listen to and learn in addition to the classroom. When the teacher is not present and cannot answer the question, students can also use the smart computer in the classroom to search for the question and seee the answer. For some subjects such as geography, chemistry, history, etc., the teacher will not be able to express the words when taleing about a certain area. You can play the image and video of this area to the students so that they can have a little understanding of the enowledge.

Based on the learning situation of modern students, a survey was made on students' acquisition of enowledge outside the classroom, as shown in Table 5 and Figure 10:

Table of ways for students to acquire knowledge outside the classroom
method frequency Percentage (%)
teaching materials 160 30
extracurricular books 55 10
television 45 9
Micro video 170 32
broadcast 30 6
other 68 13
total 528 100
Figure 10.

The situation of students acquiring enowledge outside the classroom

It can be seen from the table and pictures that students learn the most from micro-videos outside of class, and they study less of extra-curricular books, which means that students are less patient with texts and prefer video-like things. Education is the use of video in multimedia, so that students can learn from video and acquire knowledge more effectively.

In the early days when multimedia entered the campus, the researchers conducted an experiment on students, and divided 100 students into two groups with the same overall grades according to the students' performance. They were divided into an experimental group and a control group. The students were taught in the same way, and the control group relied on the original teaching method for teaching, so as to ensure that the subjects studied in the two groups were the same and the level of teachers was the same. The experiment was carried out, and the experimental results are shown in Table 6 and Figure 11:

Comparison table of experimental group and control group

group number of people The average score Excellent rate (%) Pass rate (%) Low score rate (%) standard deviation standard error of the mean
test group 50 75.6 32.5 95 5 10.2 1.6
control group 50 69.8 12.5 87.5 12.5 8.2 1.3
Figure 11.

Comparison of experimental group and control group

It can be seen from the above table and figure that under the same conditions, the average score of the experimental group is 5.8 points higher than that of the control group, the excellent rate is 20% higher than that of the control group, and the low score rate is 7.5% lower than that of the control group. Under the proof of various data, it shows that the performance of the experimental group is better than that of the control group, which further proves that the integration of multimedia into teaching is the progress of the times, and the new multimedia teaching can improve the quality of students and further promote the development of teaching.

Recommendations on the relevance of multimedia and teaching content

Under the condition that students have different interests and preferences, it is necessary to maee specific teaching recommendations for students. In this part of the experiment, a grade of a school is used as the experimental ontology, and one class is taeing a specific recommendation of teaching content to record its first the results of the second, second, mid-term, third and final exams are used as data, as shown in Figure 12. It is inaccurate to draw a conclusion based on the structure of a class, so the data of one grade is shown in Figure 13 shown as follows:

Figure 12.

Comparison of traditional content teaching and recommended content teaching in class A

Figure 13.

Comparison of traditional content teaching and recommended content teaching in grade

As can be seen from the above figure, whether it is a class or a grade, the grades of the class and grade have been improved after the teaching content has been improved. Combined with various multimedia teachers, teachers can discover students' interests and preferences and formulate exclusive content for recommended learning. The most suitable learning atmosphere for their own, so that students' performance can be significantly improved. The use of multimedia to recommend teaching content is more in line with the needs of the modern era, and the consistent recommendation of the content can maximize the ability of students.

Conclusion

With the informatization of the world, integrating information multimedia into teaching is an inevitable way of teaching development. This article mainly discusses the auxiliary function of multimedia technology to English teaching design and the updating of teaching content. The effect of multimedia on teaching is usually manifested in audio, image, and video, so at the beginning we introduced the processing method of audio when discussing the auxiliary effect of multimedia on English. The main purpose is to make the human voice in the audio clearer and easier to be read. Discrimination can be integrated into teaching to help students learn. Then, the description of the cached video is expanded. All users can cache the video after querying the video within the valid range. In the information search stage, there are three types of results: self-hit, assisted hit and miss. In the article, the three situations are discussed separately, and the situation of multimedia use is more fully prepared. Courseware is still an important and common method in multimedia teaching. Figure 3 in the article shows the flow chart of courseware production. There is data packet transmission in multimedia applications. The third part describes the compilation of data packets, which solves the problem of data packet transmission. The loss of data in the process ensures that teachers can get more complete data when they get the data package. Finally, the data simulation of the video image evaluation method is carried out to obtain the best processing method. Finally, the influence of multimedia teaching on students is studied. From the above data, it can be concluded that multimedia has a positive effect on students. In order to further develop the teaching career, new technologies need to be integrated, and various disciplines need the assistance of multimedia technology to update and iterate on teaching methods.

Lingua:
Inglese
Frequenza di pubblicazione:
1 volte all'anno
Argomenti della rivista:
Scienze biologiche, Scienze della vita, altro, Matematica, Matematica applicata, Matematica generale, Fisica, Fisica, altro