Mastering Discrete Math II: A Comprehensive Guide

Discrete Math II at WGU is a rigorous course, and learner’s journey through it in six weeks is often impressive. We listened to various students’ detailed experience and insights on social media platforms and thought it would be invaluable for those embarking on this challenging academic adventure. Let’s break down your strategies and insights to guide future students seeking success in this course.

Embrace the Materials, Expand Beyond

You’ve emphasized the utilization of course materials, including the zybook, video resources, worksheets, and cohort slides. However, you’ve also highlighted the need to supplement these resources. External videos, like the ‘don’t memorize’ series on permutations and combinations, proved beneficial. Exploring additional practice problems from various sources and seeking guidance when stuck can be game-changers.

Units Breakdown: Key Focus Areas

• Unit 1: Algorithms: Understanding Big O notation and algorithm analysis is crucial. Coding proficiency eases comprehension here, and practicing pre-assessment problems mirrors the OA.
• Unit 2: Number Theory and Cryptography: This unit demands a deep grasp of Euclid’s Algorithm, mod/div, GCD, hexadecimal, binary conversion, RSA encryption, and more. The OA is notably tougher than the pre-assessment.
• Unit 3: Recursion and Induction: Despite initial challenges, your dedication and thorough preparation led to exemplary results on the OA, which was notably harder than the pre-assessment.
• Unit 4: Counting and Advanced Techniques: Bijection, permutations, combinations, multisets, and the pigeonhole principle are pivotal here. Extra practice beyond zybook content is essential due to the immense difficulty gap between pre-assessment and OA questions.
• Unit 5: Discrete Probability: Comprehensive understanding of conditional probability, random variables, and a strong foundation in Unit 4 are prerequisites. Bayes Theorem can be complex, but focusing on other areas might compensate for its difficulty.
• Unit 6: Modeling Computation: This section provides manageable points, especially if one grasps DFA and NFA concepts thoroughly. Expect a slightly harder OA but relatively similar to the pre-assessment.

understanding Big O notation, especially in relation to loops and nested function calls, can be crucial for tackling problems in Discrete Math II:

Understanding Big O Notation and Loops

1. Worksheet Insight: The Unit 1 worksheet, particularly its answer sheet, proved valuable in comprehending Big O notation within the context of loops. It can get tricky distinguishing between linear time complexity (O(n)) and logarithmic time complexity (O(log n)), especially when a loop involves a variable(s) that’s manipulated by a constant.
2. Google Search for Big O: Supplementing worksheet insights with additional research via Google aids in solidifying understanding. This resourceful approach helps clarify various instances of Big O notation and their application within algorithms.

Application in Function Calls and Nested Loops

3. Problem Example: A specific question on both the pre-assessment and the OA involved a pseudocode that called a function within a double nested loop. The question focused on determining the dominant runtime of the pseudocode.
4. Analyzing Big O Impact: Understanding Big O notation unveils the runtime complexities of different segments:
   • The first loop operates in O(n).
   • The nested loop within it also operates in O(n).
   • The function call inside the nested loop operates in O(n log n).

Calculating Overall Complexity

5. Comprehending Dominant Runtime: By combining these complexities, the overall runtime complexity of the pseudocode is determined:
   • O(n) for the first loop * O(n) for the nested loop * O(n log n) for the function call inside the nested loop yields O(n^3 log n) as the final answer.

Importance of Worksheets for Comprehension

6. Value of Worksheets: Similar to the approach used in Discrete Math I, leveraging the course-provided worksheets greatly aids in understanding complex concepts like Big O notation. For Discrete Math I, utilizing the zybook and instructor-provided worksheets sufficed for a clear understanding of the material within four weeks.

Understanding Big O notation, especially when applied to loops and nested function calls, is essential for accurately assessing algorithmic runtime complexities. The ability to dissect and compute complexities within code segments is a valuable skill, often enhanced by dedicated practice and resource utilization such as course worksheets and external research.

Strategies for Success

Your advice to avoid rushing through the material resonates well. Patience and steady progress are key. Each unit demands dedicated attention, especially the challenging ones like Units 3, 4, and 5. Investing time in understanding the concepts deeply pays off, not just for passing the course but for future career prospects as well.

Final Thoughts and Future Outlook

The significance of the course extends beyond passing exams. Insights from family members who have pursued Computer Science at prestigious universities reinforce the practicality of the knowledge gained. Skills like understanding Big O, algorithms, and various concepts covered in Discrete Math II are highly valued in real-world job interviews and professional settings.

Conclusion

Our insights into these six-week journey through Discrete Math II at WGU provides a roadmap for success. It’s a demanding yet achievable course that requires diligence, a thorough understanding of core concepts, and a strategic approach to tackling the OA. By embracing course materials, seeking supplementary resources, and mastering each unit progressively, future students can navigate this course with confidence.

Good luck to all those embarking on this academic adventure! Your determination and persistence will undoubtedly pave the way for success, both academically and professionally.

here’s a summary of the additional advice and insights shared

Leveraging Pre-Assessment and Zybooks

1. Pre-Assessment Preparation: Engaging with the Zybooks content before attempting the pre-assessment provides a foundational understanding of the course material. It boosts confidence and familiarity, aiding in better performance.
2. Supplementary Resources: Utilizing a well-organized playlist compiled by u/Moose_Banner from subreddit content offers a structured approach. Combining this with Zybooks and Chegg for explanations on difficult questions proved beneficial. However, caution is advised as explanations might not always be accurate, and seeking further clarification from reliable sources, like ChatGPT, can help.

Targeted Study Approaches

3. Unit 6 (Modeling Computation): While resources like Zybooks suffice for this section, ensuring a thorough understanding is recommended as it’s relatively easier. Mastery here can provide easy points and buffer other challenging areas.
4. Post-Pre-Assessment Review: After studying with playlists and Zybooks, attempting the pre-assessment again is advised. Additionally, engaging with the Course Planning Tool (CPT) questions post pre-assessment success reinforces understanding and prepares for variations of similar questions that might appear in the Objective Assessment (OA).
5. Adapting Study Techniques: Recognizing that learning styles differ, the advice is adaptable. Tailoring study methods to individual preferences and strengths is crucial for effective learning.

Tips for OA Execution

6. Effective Time Management: Utilize the entire exam duration wisely. Bookmarking challenging or time-consuming questions aids in revisiting and ensuring accuracy, especially for calculations.
7. Unit-specific Challenges: Areas like Recursion and Induction (Unit 3) and Counting and Advanced Counting Techniques (Unit 4) might present different challenges in the OA compared to the pre-assessment. Being prepared for potential shifts in question styles or approaches is essential.

Parting Words

The closing emphasis on individual learning preferences and adaptability stresses the importance of customizing study techniques. Wishing luck to fellow students embarking on similar academic endeavors is a positive and encouraging way to conclude the advice.

Remember, the journey through Discrete Math II is a personal one, and strategies that work for one may need adjustment for another. Stay adaptable, resilient, and best of luck with your academic pursuits!