# Is Discrete Structures Harder Than Linear Algebra?

Mathematics is a diverse field that encompasses several branches, including calculus, linear algebra, and discrete structures. These subjects are often studied by individuals seeking careers in related fields like engineering, computer science, physics, and economics, to name a few. Among these branches, Discrete Structures and Linear Algebra are two that are often compared, with many people wondering which one is more difficult. In this article, we aim to answer this question based on various factors like course content and cognitive complexity, among others.

## FAQs

### What is Discrete Structures?

Discrete Structures deal with distinct, disconnected objects, which are finite or countable. Topics covered in Discrete Structures include logic, set theory, graphs, algorithms, number theory, permutations, and combinations. These concepts are applicable in various fields like computer science, cryptography, and data analysis, among others.

### What is Linear Algebra?

Linear Algebra deals with linear equations and their solutions. Topics covered in Linear Algebra include vectors, matrices, determinants, eigenvalues, and eigenvectors, and linear transformations. These concepts are applicable in various fields like mechanics, physics, economics, and computer graphics, among others.

### How do Discrete Structures and Linear Algebra Compare?

Comparing these two subjects, we can say that Discrete Structures are more diverse than Linear Algebra. Discrete Structures cover a wide range of topics, while Linear Alegbra focuses more on matrices, vectors, and linear equations. Discrete Structures require students to apply different methods and techniques, while Linear Algebra necessitates consistent use of one or two concepts repeatedly.

### Which is Harder – Discrete Structures or Linear Algebra?

Some individuals find Discrete Structures harder, while others find Linear Algebra more challenging. However, when analyzing various factors like content complexity, cognitive demand, and student feedback, we can conclude that Discrete Structures are generally more tricky than Linear Algebra.

## Factors That Make Discrete Structures Harder

### Cognitive Complexity

One thing that makes Discrete Structures harder is that it involves more abstract and complex concepts that require a high level of cognitive demand. Students studying Discrete Structures must possess a higher level of critical thinking and problem-solving skills to solve problems concerning graphs, algorithms, sets, and logic, among others. Additionally, the highly abstract nature of Discrete Structures makes it more difficult to apply the concepts learned in real-world situations.

### Diversity of topics

Discrete Structures involve a wide range of topics that may not be directly related. Students require a high level of versatility in understanding and applying various methods and techniques to solve related problems on permutations, combinations, probability, and logic, among others. The variety of topics in Discrete Structures makes it harder for students to stay engaged and keep up with the course content.

### Student Feedback

Feedback from students who have taken Discrete Structures courses validates the general consensus that it is harder than Linear Algebra. Discrete Structures courses often have lower grade distributions and higher midterm and final exam averages than Linear Algebra courses. Additionally, students studying Discrete Structures report spending more time on assignments and struggle with challenging topics like logic, algorithms, and set theory.

## Conclusion

In summary, comparing Discrete Structures with Linear Algebra, we can say that Discrete Structures are generally harder due to various factors, including cognitive complexity, variety of topics, and overall student feedback. However, this does not imply that Linear Algebra is easy. Linear Algebra still involves some challenging concepts, and mastering it requires a high level of analytical and mathematical skills. Ultimately, the difficulty of Discrete Structures or Linear Algebra depends on individual preference and prior mathematical background.

## References

- Discrete Mathematics by Glen E. Zwick
- Linear Algebra by Thomas Neylon
- Linear Algebra in Biology by Michelle Girvan