2023-11-12

Trust is your own stride, Luck’s but a fleeting whisper, Confidence shouts loud.

Biggest takeaway from yesterday: It’s important to get for a walk to clear your head sometimes :-) Daily Note Generation

Morning Briefing (2023-11-12) §

Current weather in Lincoln, UK is heavy intensity drizzle with a temperature of 7.62°C. Overall forecast for Lincoln, UK today is light rain with an average temperature of 10.4°C.

Global News §

• Peter Nygard: Fashion mogul guilty of sex assaults
• Israel-Hamas War: A Major Gaza Hospital Is ‘Out of Service,’ Red Crescent Says
• Who will foot the bill for the devastation caused by Israel’s war on Gaza?
• NHK WORLD RADIO JAPAN - English News at 04:30 (JST), November 13
• Spain’s conservatives rally against deal with Catalan separatists

Lincoln News §

• Rishi Sunak says government is ‘squarely’ investing in Lincolnshire’s infrastructure
• How Lincolnshire is committed to wildlife conservation for years to come
• ‘Dearest dad’ among death notices and funeral announcements from Lincolnshire Echo this week
• The Beatles’ final harmony: ‘Now And Then’ tops charts, reviving vinyl fever in Lincolnshire
• Free parking offer across Lincoln in the lead up to Christmas

Mathematical News §

• Yucatán’s underwater caves host diverse microbial communities
• Designing cities for 21st-century weather
• Explaining Wildfires Through Curvature
• Compactifications, Configurations, and Cohomology
• Hummingbirds’ unique sideways flutter gets them through small apertures

Daily Job Market Trends §

Currently, the job market for maths graduates in Lincoln, UK is showing positive growth. There is a high demand for mathematical skills in various industries such as finance, data analysis, technology, and engineering. Companies are seeking candidates who possess strong analytical abilities, problem-solving skills, and a solid understanding of mathematical theory.

Available Scholarships or Grants §

Several scholarships and grants are available for further mathematics studies in Lincoln, UK. Here are a few notable ones:

• University of Lincoln Scholarships: The university offers various scholarships for postgraduate students, including those pursuing mathematics-related programs.
• Newton International Fellowships: This fellowship program supports early-career mathematicians who wish to pursue research projects in the UK.
• Royal Society Dorothy Hodgkin Fellowship: Designed for outstanding mathematicians who require flexible working arrangements for research.

Upcoming Maths Conferences or Workshops §

Stay tuned for the following upcoming maths conferences and workshops in Lincoln, UK:

• Mathematical Institute Conference: This annual event brings together researchers, academics, and professionals from various mathematical disciplines.
• Maths and Industry Study Groups: These workshops provide opportunities for collaboration between mathematicians and industry professionals to solve real-world problems.

Career Advice for a Maths Student §

For maths students looking to build successful careers, consider the following advice:

1. Networking: Connect with professionals in mathematics-related fields through networking events, online platforms, or industry conferences.
2. Internships: Gain practical experience through internships or part-time positions to enhance your skills and make industry connections.
3. Continual Learning: Stay up-to-date with emerging trends, new technologies, and advancements in mathematics through continuous learning and professional development opportunities.
4. Problem-solving: Sharpen your problem-solving skills by challenging yourself with complex mathematical problems and participating in competitions.
5. Collaboration: Seek opportunities to collaborate with peers and professionals from diverse backgrounds to develop skills in teamwork and communication.

Remember, perseverance and a passion for mathematics will pave the way for a successful career in the field. Good luck!

Today’s Maths Problem §

Problem:

Consider a function $f(x)=x^3-3x^2-10x+8$.

Find the x-intercepts of $f(x)$ and determine whether each intercept is a local maximum or local minimum point.

Solution:

To find the x-intercepts of $f(x)$, we set $f(x)=0$:

$x^3-3x^2-10x+8=0$

This equation can be factored as:

$(x-4)(x+1)(x-2)=0$

Setting each factor equal to zero, we find three solutions:

$x-4=0⟹x=4$

$x+1=0⟹x=-1$

$x-2=0⟹x=2$

So, the x-intercepts are at $(4,0)$, $(-1,0)$, and $(2,0)$.

To determine whether each intercept is a local maximum or local minimum point, we can use the first derivative test.

Taking the derivative of $f(x)$ with respect to $x$, we have:

$f^{\prime }(x)=3x^2-6x-10$

Setting $f^{\prime }(x)=0$ and solving for $x$, we find:

$3x^2-6x-10=0$

This quadratic equation does not factor easily, so we can use the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In this case, $a=3$, $b=-6$, and $c=-10$. Plugging in these values, we get:

$x=\frac{-(-6)\pm \sqrt{(-6{)}^2-4(3)(-10)}}{2(3)}$

Simplifying further, we find two solutions for $x$:

$x=\frac{3\pm \sqrt{69}}{3}$

The values of $x$ obtained from this equation correspond to critical points of $f(x)$.

The x-intercepts are at $x=4$, $x=-1$, and $x=2$.

By evaluating $f^{\prime \prime }(x)$ at these three points, we can determine whether each intercept is a local maximum or local minimum point.

Taking the second derivative of $f(x)$ with respect to $x$, we have:

$f^{\prime \prime }(x)=6x-6$

Evaluating $f^{\prime \prime }(x)$ at $x=4$, $x=-1$, and $x=2$, we find:

$f^{\prime \prime }(4)=18$

$f^{\prime \prime }(-1)=-12$

$f^{\prime \prime }(2)=6$

Since $f^{\prime \prime }(4)>0$, $f^{\prime \prime }(-1)<0$, and $f^{\prime \prime }(2)>0$, we can conclude that the x-intercept at $x=4$ is a local minimum point, the x-intercept at $x=-1$ is a local maximum point, and the x-intercept at $x=2$ is a local minimum point.

Today’s Schedule §

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Based on my experiences as a maths student, I understand the ups and downs that come with exam stress. Today, I believe your day will be challenging but ultimately productive. You may feel a bit overwhelmed at times, but with determination and focus, you will make progress in your studies. Remember, tackling one task at a time and taking short breaks to recharge your mind will help alleviate the stress. Stay confident in your abilities, and you will succeed.

Chess Puzzle & Games §

Chess Puzzle §

Rating: 1447 Puzzle ID: WIB16

fen: 3r4/6pk/p1R4p/3P1q2/4pp2/1B6/P4PPP/3R1K2 b - - 3 35

Solution §

['e4e3', 'b3c2', 'f5c2', 'c6c2']

Chess Games §

A space to log what chess games I’ve done today, as well as an analysis of them.

…

Good Luck! ✨ §

Good luck, my friend! Believe in yourself, trust your instincts, and give it your all. Remember that every step forward is progress, and with your determination, there’s nothing you can’t achieve. Go out there and make your dreams a reality! You’ve got this! 🌟

Now… §

Have a look at the to-do list in The Scholar’s Ledger, or try some yoga/home calisthenics.

Sure! Here are five random, fun emojis for you: 🤪🎉🍕😂🦄 Enjoy!

Archived §

• Re-vamp Daily Note Template and my Google Calendar with Honeyman Method (note that I’ve learned of this before she conceived of the idea, so I’m not sure who to attribute it to - I’ve forgotten where I learned it): possible routines. 🔒 2023-11-12 🕸️ The Scholar’s Ledger
• Create a legend: Slave -> Overlord (Shadow of War): Link to idea 🔒 2023-11-12 🕸️ The Scholar’s Ledger