Why do you want to study group theory after studying chemistry?

Answer the first question first. Chemistry, as a natural science, must try to follow the mathematical system, to put it bluntly, as formulaic as possible. As a discipline in the middle of the natural sciences, chemistry is striving to express experimental facts and laws in physical models, which are basically highly mathematical.

Specifically, the branch of computational chemistry focuses on studying molecular interactions (mainly electromagnetic) on the basis of quantum physical models, modeling, and leading results. This part of the research is still in a relatively early stage, and it can study the simple interactions of some molecules that are not too large, but it is far from the extent that it can achieve experimental results (compared with high-energy physics, experimental physics, condensed matter physics, etc.).

In the foreseeable future, computational chemistry research will make progress, but in the short term, it is impossible to replace the mainstream chemical laboratory research (personal opinion). This is mainly because of the complexity of the real world, as well as the quantitative scale of the macro system. To a large extent, the bottleneck may lie in human computing power; However, if the computational cost is too high, it will lose its advantages as a research method compared with experimental research.

The second question is how much mathematical foundation is needed for those who work in chemistry-related subjects.

For most people, the meaning of mathematical foundations is very limited. The following is described in the order in which they are studied.

In the secondary disciplines of chemistry, physical chemistry and structural chemistry are generally considered to have high mathematical requirements. Physical chemistry does involve some of the calculus, but most of it is only a superficial concept. For example, in a one-component system, (e.g., a pure gas), enthalpy (h) can be expressed as a function of pressure p and temperature t.

Based on this, a fully differential expression is often written, and then the change in enthalpy is discussed when a certain condition changes. To complete this part of the reasoning, you only need to have the most basic concepts of total differentiation. In fact, mathematics that is slightly lower than engineering is beyond what needs to be used - there is no such thing as a "continuous and inderivable" or "infinite series" state in the real world!

In this way, it is reasonable not to make excessive mathematical requirements as a compulsory subject.

It is important to emphasize that this discussion is not to deny the importance of mathematics, but to clarify that it is generally reasonable for chemistry students to have low mathematical requirements in terms of practicality and universality of education. The "chemistry" discussed above refers to "chemistry" in the sense of science, that is, it does not involve industrial research and development. Chemical engineering has special requirements for mathematics, and due to the limitations of my major, I should not analyze it arbitrarily.

If it is only basic inorganic chemistry, it does not require a high level of mathematical knowledge, and further study of analytical chemistry, physical chemistry, structural chemistry, etc., it requires advanced mathematical knowledge.

Chemistry majors depend on what direction you are studying, and some directions still have high mathematical requirements, such as physical chemistry, structural chemistry, quantum chemistry, etc.

Why? Chemistry also has high requirements for mathematics, and it seems that I haven't learned it deeply.

Chemistry is a college major. The major of chemistry cultivates high-level professionals who have the basic knowledge, basic theories and basic skills of chemistry, and can engage in scientific research, teaching technology and related management in chemistry and chemistry-related science and technology and other fields.

Group Theory Definition: In mathematics and abstract algebra, group theory studies the algebraic structure called groups. Groups have a fundamental importance in abstract algebra:

Many algebraic structures, including rings, fields, and modulos, can be seen as being formed by adding new operations and axioms to groups. The concept of groups is present in many branches of mathematics, and the research methods of group theory have also had an important influence on other branches of abstract algebra. The importance of group theory is also reflected in the study of physics and chemistry, as many different physical structures, such as crystal structures and hydrogen atomic structures, can be modeled using group theory methods.

As a result, group theory and related group representation theory have a large number of applications in physics and chemistry.

Group theory covers a wide range of topics and requires a lot of basic knowledge, such as: set-related knowledge, geometry, topology, mathematical analysis, algebra, probability theory, operations research, applied statistics, etc.

Therefore, if you want to study, it is best to choose a direction for research, otherwise too much knowledge is not conducive to research and learning.

Theoretically, you don't need any basic knowledge, and you can learn math on your own after studying high school. Of course, if you learn linear algebra first, it will help you understand the concept. It is said that the "Group Theory" written by Han Qizhi and Sun Hongzhou was written for the physics and chemistry major, so you might as well give it a try.

The basis of irreducible representation depends on the object under consideration. The choice of the base is different depending on the object.

The common basis vectors in chemistry are none other than DiCar's coordinates x, y, z or atomic orbitals.

In the C3V feature table, an irreducible basis of A1G can be the Z-axis in the DiCar's coordinates (assuming that the Z-axis is the C3 axis of rotation), the Pz orbital of the nitrogen atom in the NH3 molecule (listed in the III region), or the transition metal in the C3V MCL3 molecule.

The dz2 orbital of the atom (in the iv region). At the same time, a set of (two-dimensional) bases of a two-dimensional irreducible representation e can be the (x, y) axis in DiCar's coordinates (assuming that the z-axis is the C3 axis of rotation), the (px,py) orbital of the nitrogen atom in the NH3 molecule (listed in the III region), or the (DX2-Y2,DXY) orbital of the transition metal atom in the C3V MCl3 molecule, or the (DXZ, DYZ) orbital (in the IV region).

In addition, region III illustrates the infrared-active properties; Region IV Raman active properties.

In the second grade, I will take a course called "Physical Chemistry", which is basically all calculus calculations.

If you continue to study in depth, structural chemistry will use very difficult advanced mathematical knowledge, and linear algebra and group theory are also widely used in structural chemistry.

Suffice it to say, chemistry is not good either.

We know that group theory is an important branch of mathematics, and it has important applications in many disciplines, such as in physics, and group theory is the foundation of quantum mechanics. The purpose of this course is to provide students with a perceptual understanding and a rational understanding of the basic theories of group theory. This course introduces the basic theories and applications of group theory.

The main contents are: firstly, the concepts of groups, subgroups, group isomorphism and related properties are introduced, which is the first step to understand groups. The two most common groups are then discussed in some detail:

Cyclic groups and permutation groups, including some examples and exercises, can familiarize yourself with the operation and properties of groups, and deepen your understanding of groups. Some applications of permutation groups are also introduced.

Then, some important concepts in group theory are discussed. First, the operation of a subset of the group is defined and discussed. Based on the operation of the subset of the group, the concept and nature of the co-set of the subgroup are introduced and discussed. The concepts and properties of formal subgroups and quotient groups are defined and discussed.

With the help of the concept of quotient group, the basic theorem of group homomorphism is proved, and the homomorphism of group is systematically described. This part of the content is the most basic content of group theory, and it must be mastered by any reader who wishes to learn group theory. The concept of the direct product of the group is also given, which is an indispensable tool for studying the structure of the group.

Give you the title of each chapter.

Inorganic Chemistry Fundamentals of Chemistry.

Fundamentals of Chemical Thermodynamics.

The rate of chemical reactions.

Chemical equilibrium. Atomic structure and periodic law.

Chemical bond theory.

Acid-base dissociation equilibrium.

Precipitation dissolves equilibrium.

Redox reactions.

Coordination compound.

Elemental chemistry fraction (alkali metals, alkaline earth metals, boron, carbon, nitrogen, oxygen, halogen, hydrogen and noble gases, copper-zinc subgroup, chromium-manganese subgroup, iron-based, platinum-based, titanium-vanadium subgroup, lanthanide, actinides).

Organic Chemistry Classification of organic compounds Representation Naming.

Stereochemistry. Alkanes are free radical substitution reactions.

Ultraviolet spectroscopy, infrared spectroscopy, nuclear magnetic resonance and mass spectrometry.

Nucleophilic substitution reaction on aliphatic saturated carbon atom - elimination of reaction halogenated hydrocarbons organometallic compounds.

Olefins Electrophilic Addition Free Radical Addition Conjugated Addition.

Alkyne alcohols and ethers.

Benzene and aromatic hydrocarbons are aromatic electrophilic substitution reactions.

Aldehydes and ketones nucleophilic additions.

Carboxylic acids carboxylic acid derivatives nucleophilic substitution reactions on acyl carbons.

Carboanion condensation reaction.

Pericyclic reaction. Amine nitrogenous aromatic compounds aromatic nucleophilic substitution reaction.

Phenol and quinone heterocyclic compounds.

Monosaccharides, oligosaccharides, and polysaccharides.

Amino acids, peptides, proteins, enzymes, and nucleic acids.

Terpenoids: Steroid compounds and alkaloids.

Analytical Chemistry: Introduction to Quantitative Analytical Chemistry.

Acid-base balance and acid-base titration.

Complexation titration.

Redox titration.

Gravimetric analysis and precipitation titration.

Absorbance.

Data processing in analytical chemistry.

Separation and enrichment methods commonly used in analytical chemistry.

Physical Chemistry: The First Law of Gas Thermodynamics.

The second law of thermodynamics.

The solution phase is equilibrate.

Chemical equilibrium. Fundamentals of Statistical Thermodynamics.

Electrolyte solution.

Reversible electromotive force for batteries and their applications.

Point solution and polarization.

Chemical kinetics.

Surface Physical Chemistry.

Colloidal dispersions and macromolecular solutions.

Structural Chemistry: Fundamentals of Quantum Mechanics.

Atomic structure. Diatomic Molecular Structure and Chemical Bond Theory.

Molecular symmetry and group theory preliminary.

Structure and properties of polyatomic molecules.

Lattice structure of crystals with X-ray diffraction.

The structure of metal crystals and ionic crystals.

A brief introduction to the structure of the new material.

Principles of structural analysis.

That's all, I hope it works for you.

In fact, "Organic Chemistry" and "College Chemistry" can be the titles of books, go to the library and look for them.