Mathematics and Research
13 subscribers
11 photos
2 videos
66 links
Explore math with us! We share PhD & job opportunities, learning resources, open-source tools, and fun math content.
Download Telegram
In the empirical probability approach, the probabilities are based on observed data, not
on prior knowledge of a process. Surveys are often used to generate empirical probabilities.

Examples of this type of probability are the proportion of individuals in the Using Statistics
scenario who actually purchase big-screen televisions, the proportion of registered voters who
prefer a certain political candidate, and the proportion of students who have part-time jobs.

For example, if you take a survey of students, and 60% state that they have part-time jobs, then
there is a 0.60 probability that an individual student has a part-time job.


The third approach to probability, subjective probability, differs from the other two
approaches because subjective probability differs from person to person. For example, the
development team for a new product may assign a probability of 0.60 to the chance of success
for the product, while the president of the company may be less optimistic and assign a probability of 0.30. The assignment of subjective probabilities to various outcomes is usually based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation. Subjective probability is especially useful in making decisions in situations in
which you cannot use a priori probability or empirical probability
Max Planck Institute for Mathematics
https://www.mpim-bonn.mpg.de/
📌Quantitative Data Analysis

📌Descriptive Statistics:

📍What it is: Techniques used to summarize and describe the main features of a collection of data.

📍What it does: It presents the data in a way that is easily understandable, often using measures of central tendency (mean, median, mode) and measures of variability or spread (standard deviation, variance, range). It does not draw conclusions beyond the data itself.

📌Inferential Statistics:

📍What it is: Methods that allow researchers to use data collected from a sample to make inferences or draw conclusions about a larger population.

📍What it does: It involves hypothesis testing, estimation of population parameters (like confidence intervals), and making predictions. It's about generalizing from a smaller group to a larger one.

📌Regression Analysis:

📍What it is: A set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

📍What it does: It helps to understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. It's often used for prediction and forecasting.

📌ANOVA (Analysis of Variance):

📍What it is: A statistical test used to compare the means of two or more independent groups to determine if the differences between them are statistically significant.

📍What it does: It does this by analyzing the variation within each group compared to the variation between the group means. For example, testing if the average scores of three different teaching methods are all equal.

📌Chi-Square Test:

📍What it is: A non-parametric statistical test primarily used to examine the relationship between two categorical variables.

📍What it does: The most common form (Chi-Square Test for Independence) determines if there is a significant association or difference between the observed frequencies and the frequencies that would be expected if the variables were independent.

📌Factor Analysis:

📍What it is: A statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.

📍What it does: It is a data reduction technique that seeks to find underlying dimensions or "factors" that explain the patterns of correlations among a large set of measured variables. It is often used in survey research and psychometrics.

@mathandresearch
Dear colleagues!

We are pleased to announce that our upcoming International Research Seminar will be launched with the talk by Professor Shavkat Alimov.

Please, visit the new website of the seminar (https://sites.google.com/view/int-research-seminar/home) and if you would like to give a talk, please register yourself using the registration form.

Below are details of the talk:

🔹 Speaker
Name
: Professor Shavkat Alimov
Affiliation: National University of Uzbekistan and V.I.Romanovskiy Institute of Mathematics
🔹 Title of the Talk
"On the correctness of the Cauchy problem for the fractional Weyl derivative equation"
🔹 Abstract
The Cauchy problem for the partial differential equation with Weyl fractional derivative of order $\alpha$ is considered. Conditions on the order of $\alpha$ are found, under which the task is well-posed in Sobolev classes. In other cases, solvability in Gevrey classes is proved. The conditions for the $\sigma$ exponent of the Gevrey class and the order of $\alpha$ are found, under which the problem under consideration is well-posed.

🔹 Date & Time
Date: Wednesday, October 8, 2025]
Time: 16:00 (GMT+5 Tashkent)
, 14:00 (GMT+3 Moscow), 13:00 (GMT+1 Brussel)
🔹 Join via Zoom
🔗 Zoom Link: https://us06web.zoom.us/j/88273567781?pwd=6TMH3UOjALVQmLsLlm6vTMPo5YpCYr.1

Meeting ID: 882 7356 7781
Passcode: 151325

Sincerely,
the Secretary of the seminar
DSc Rakhimjon Zunnunov
Teaching opportunity in Saudi Arabia. Itqan college.
Use link to apply
https://forms.gle/MvJFCiz2ZVE2JebWA
A very beautiful problem in Integral Calculus.

https://t.iss.one/mathandresearch
All other programs except psychology are in English and hence don't require HSK. This scholarship is more than ANSO China. Supervisors will provide an annual allowance of at least 12,000 CNY for their recruited international doctoral candidates, which will be used for scientific research subsidies or academic exchanges.

First-class honor
Tuition waiver + living allowance of 6000 CNY/month
Second-class honors
Tuition waiver + living allowance of 5000 CNY/month
Third-class honor
Tuition waiver + living allowance of 4000 CNY/month
https://en.szu.edu.cn/info/1024/1845.htm
🔗 Link
https://en.szu.edu.cn/info/1024/1845.htm?fbclid=IwdGRzaAN47tNjbGNrA3jucmV4dG4DYWVtAjExAHNydGMGYXBwX2lkDDM1MDY4NTUzMTcyOAABHqdzjaTanZew8326YDPCjJAe-XpLaR_JGmxtdQEA7ZLRgg4noWLbOMinUcxD_aem_bK3WXpyWSaFZ2MQYuPJzCA