1. Abstract thinking: Abstract thinking is emphasized in college mathematics, that is, concrete problems are transformed into abstract mathematical models, and problems are described and solved with symbols and formulas.

2. Logical reasoning: College mathematics pays attention to the cultivation of logical reasoning ability, and students need to learn to use known theorems and properties to deduce and prove, so as to draw new conclusions.

3. Analysis and synthesis: College mathematics requires students to analyze the essence and characteristics of the problem, break it down into smaller parts for research, and then synthesize all parts to get the overall solution.

4. Spatial imagination: Geometry and linear algebra in college mathematics require students to have certain spatial imagination ability, and can transform abstract mathematical concepts into concrete figures or vectors.

5. Mathematical modeling: In college mathematics learning, students need to learn to turn practical problems into mathematical models and use the mathematical knowledge and methods they have learned to solve practical problems.

6. Mathematical symbols and languages: College mathematics uses specific symbols and languages to express mathematical concepts and relationships, and students need to master the meaning and usage of these symbols and languages skillfully.

7. Mathematical proof: In college mathematics learning, students need to learn to use logical reasoning and mathematical theorems to prove, so as to ensure the correctness of the conclusion.

In a word, the basic concepts and thinking methods of college mathematics learning include abstract thinking, logical reasoning, analysis and synthesis, spatial imagination, mathematical modeling, mathematical symbols and languages, and mathematical proof. Mastering these basic concepts and thinking methods is very important for learning college mathematics well.