1. Solving linear systems using elementary row operations, matrix operations.
2. Row equivalence, the inverse matrix and related topics.
3. Determinants and its applications.
4. Real vector spaces, the concept of linear independence, basis.
5. Linear transformation and related topics.

1. Solving linear systems using elementary row operations, matrix operations.
2. Row equivalent, the inverse matrix and related topics.
3. Determinants and its applications.
4. Real vector spaces, the concept of linear independence, basis.
5. Linear transformation and related topics.

Sampling is widely used in the modern world. The statistical offices of many nations have sample surveys conducted on topics of interest such as unemployment, size of labor force etc.. Furthermore, sample surveys are often conducted by company on topics of the behavior of consumers.
Sampling design determines the precision of the estimates. Thus, the way a sample is drawn is as important as the mathematical form of the estimator. Sample design consists of both a sample selection plan and an estimation procedure. In this course, we shall first define population, sampling units (primary, secondary, etc.); then introduce many sampling schemes, such as simple random sampling (with or without replacement), stratified sampling (optimum allocation of sampling units to various strata), multistage sampling (e.g. two-stage stratified cluster sampling), systematic sampling, double sampling, and sampling with unequal probabilities (with or without replacement). We shall also introduce ratio estimator, regression estimator, and poststratification estimators.
Finally, we shall derive the variances of the proposed estimators and the estimators of their variances. For estimating the variance of the estimators, the topics of Jackknife method and bootstrap method are also included in this course.

Sampling is widely used in the modern world. The statistical offices of many nations have sample surveys conducted on topics of interest such as unemployment, size of labor force etc.. Further, sample surveys are often conducted by company on topics of the behavior of consumers.
Sampling design determines the precision of the estimates. Thus, the way a sample is drawn is as important as the mathematical form of the estimator. Sample design consists of both a sample selection plan and an estimation procedure. In this course, we shall first define population, sampling units (primary, secondary, etc.); then introduce many sampling schemes, such as simple random sampling (with or without replacement), stratified sampling (optimum allocation of sampling units to various strata), multistage sampling (e.g. two-stage stratified cluster sampling), systematic sampling, double sampling, and sampling with unequal probability (with or without replacement). We shall also introduce ratio estimator, regression estimator, and poststratification estimators.
Finally, we shall derive the variations of the proposed estimators and the estimators of their variations. For estimating the variation of the estimators, the topics of Jackknife method and bootstrap method are also included in this course.

Elementary linear algebra with applications, B. Kolman and D. Hill, Pearson International.

Elementary linear algebra with applications, B. Kolman and D. Hill, Pearson International.