Following my conversation in comments with Mehrdad on his answer, I feel I should provide my own answer; there are in fact philosophic sides to this question which admit of a wider interpretation than the classification prevailing amongst modern Computer Scientists.
To address your exact statement (emphasis added):
I have a firm belief that Computer Science or Theoretical Computer Science is a direct branch of Mathematics and Logic and also of the opinion that a Computer Science degree has always to be Math oriented as a matter of fact. Please correct me if I am wrong.
Your classification disagrees with Wikipedia and with many modern Computer Scientists, but does that mean that it is wrong? Not necessarily. Even Wikipedia itself acknowledges opposing views on this subject, including your own view, which I share.
First let's consider definitions. (Emphasis is added.) Each of these excerpts is taken from Wikipedia; links are provided in the first word or phrase of each excerpt.
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Contemporary science is typically subdivided into the natural sciences, which study the material universe; the social sciences, which study people and societies; and the formal sciences, which study logic and mathematics. The formal sciences are often excluded as they do not depend on empirical observations.
And further (from a different page):
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof.
Today, no consensus on the definition of mathematics prevails, even among professionals.
Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science....
And now, as to CS:
Theoretical computer science is a division or subset of general computer science and mathematics that focuses on more abstract or mathematical aspects of computing and includes the theory of computation.
According to the Wikipedia article on "Branches of Science,":
Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world (empirical knowledge), but rather with the properties of formal systems based on definitions and rules.
The classification there goes on to specify theoretical computer science as a branch of formal science, alongside of mathematics.
However, given the clear fact that mathematics has no generally accepted definition but certainly involves mathematical (formal) proofs, it would not be outrageous to include everything in the "formal sciences" classification within the scope of the definition of "mathematics," as you seem to do.
My own definitions (classifications) exclude "formal sciences" from the scope of "science," for the above-cited reason that they do not depend on empirical observations.
Further, my own definition of "mathematics" includes within its scope the entirety of the so-called "formal sciences," including Computer Science.
The differentiation I would make between these terms is that science is empirical; mathematics is based on deductions from primary assumptions.
The validity of science is based on the accuracy of observations.
The applicability of mathematics depends upon the applicability of primary assumptions.